capbtabboxtable[][]

# Amenity complexity and urban locations
of socio-economic mixing

Sándor Juhász  Complexity Science Hub Vienna, Vienna, Austria  NETI Lab,
Corvinus University of Budapest, Budapest, Hungary  ANET Lab, ELKH Center for
Economic and Regional Sciences, Budapest, Hungary  Corresponding author:
<EMAIL_ADDRESS>0000-0003-3124-8597 Gergő Pintér  NETI Lab, Corvinus
University of Budapest, Budapest, Hungary  0000-0003-4731-3816 Ádám Kovács
ANET Lab, ELKH Center for Economic and Regional Sciences, Budapest, Hungary
0000-0001-6503-3047 Endre Borza  ANET Lab, ELKH Center for Economic and
Regional Sciences, Budapest, Hungary  0000-0002-8804-4520
Gergely Mónus  NETI Lab, Corvinus University of Budapest, Budapest, Hungary
0000-0002-4768-736X László Lőrincz  NETI Lab, Corvinus University of Budapest,
Budapest, Hungary  ANET Lab, ELKH Center for Economic and Regional Sciences,
Budapest, Hungary  0000-0003-4528-0918 Balázs Lengyel  NETI Lab, Corvinus
University of Budapest, Budapest, Hungary  ANET Lab, ELKH Center for Economic
and Regional Sciences, Budapest, Hungary  0000-0001-5196-5599

###### Abstract

Cities host diverse people and their mixing is the engine of prosperity. In
turn, segregation and inequalities are common features of most cities and
locations that enable the meeting of people with different socio-economic
status are key for urban inclusion. In this study, we adopt the concept of
economic complexity to quantify the sophistication of amenity supply at urban
locations. We propose that neighborhood complexity and amenity complexity are
connected to the ability of locations to attract diverse visitors from various
socio-economic backgrounds across the city. We construct the measures of
amenity complexity based on the local portfolio of diverse and non-ubiquitous
amenities in Budapest, Hungary. Socio-economic mixing at visited third places
is investigated by tracing the daily mobility of individuals and by
characterizing their status by the real-estate price of their home locations.
Results suggest that measures of ubiquity and diversity of amenities do not,
but neighborhood complexity and amenity complexity are correlated with the
urban centrality of locations. Urban centrality is a strong predictor of
socio-economic mixing, but both neighborhood complexity and amenity complexity
add further explanatory power to our models. Our work combines urban mobility
data with economic complexity thinking to show that the diversity of non-
ubiquitous amenities, central locations, and the potentials for socio-economic
mixing are interrelated.

##  1 Introduction

Diversity is the key ingredient of successful and resilient cities [26]. The
spatially concentrated interaction of people from various social and economic
background create environments that foster creativity [18], support inclusion
[8] and in general, make cities vivid and prosperous [19]. At the same time,
cities show high levels of segregation such that individuals from different
socio-economic background are separated from each other in the urban space
[34]. This phenomenon limits social mobility for many [31] and induced
inequalities can expose segregated groups to health or climate crises [45, 29]
and can imply radicalization and populism [1, 17].

Recent studies leverage GPS mobility data to study socio-economic segregation
and mixing patterns in visited urban locations [11]. This growing literature
frequently reports that people in cities visit and interact with locations
that are similar to their residential neighborhood in terms of income,
education, ethnicity or other socio-economic features [48, 16, 9, 24].
However, the places, services or amenities that individuals visit in the city
exhibit different levels of experienced segregation, as some locations mix
different socio-economic groups while others do not [5, 33].

In this study we characterize urban locations that foster socio-economic
mixing and lower experienced segregation by attracting people from diverse
strata. To do so, we emphasize two aspects of urban locations that can
influence observed socio-economic mixing: their amenity portfolio and
geographical centrality in the city.

The type of amenities available at a location determine its purpose and
function and therefore is related to experienced segregation. [36] illustrates
through individual GPS trajectories that urban locations offering
entertainment amenities, services or natural water features are visited by a
more diverse set of people. [5] describes that individuals can experience
relatively low experienced segregation at outdoor places like parks, sports
fields and playgrounds, or at commercial establishments such as restaurants,
bars and retail stores. They find that places of entertainment, like theaters
and accommodations, like hotels are the least segregated urban locations. [33]
shows that the category of places is a strong predictor for experienced income
segregation and unique places in cities, such as arts venues, museums or
airports tend to be highly integrative, while places that primarily serve
local communities, such as grocery stores or places of worship are generally
more segregated by income. Yet, urban locations can be hardly described by
single amenity types; instead, they typically host more types of amenities.
Despite previous empirical efforts, systematic examination on how the mixture
of amenities at specific urban locations contribute to social mixing is still
missing from the literature.

Specialized amenities that serve the specific needs of the wider public and
therefore can attract people from diverse neighborhoods tend to situate in the
center of cities. The central place theory originally developed for the inter-
urban scale by [15] and [28] explains the hierarchy of cities and towns
through their size and the range of functions that they provide and has been
used to study the functions of locations within cities too (see for example
[47]). Higher-order centers attract population from a larger area, because
they not only share most of the functions of lower order centers, but also
host some more specialized functions too. Building on the central place
theory, [49] combines density, the number of people attracted to locations and
diversity, the range of activities that they engage with at these locations in
a single centrality measure to identify urban centers in Singapore and
illustrate their evolution over time. [36] shows that urban locations with
higher centrality in urban road networks attract more diverse visitors. On the
contrary, [33] presents that urban locations with higher average travel
distance to them tend to be less segregated than locations that are highly
accessible. While most of the studies highlight that accessible, central
locations attract more diverse visitors, yet, the nature of the available
amenity mix might be related to the position of locations, which has not been
focused on so far.

Here, we aim to extend the above literature by investigating how the available
amenities and central position of urban locations are related to experienced
segregation or, put it differently, to the mixing of people from diverse
socio-economic strata. A new contribution is the application of the economic
complexity framework to urban amenities [21] to quantify the sophistication of
local amenity supply. We argue that more complex neighborhoods and amenities
attract visitors of diverse socio-economic status from across the city.

The concept of economic complexity is originally developed by [23] who defined
complexity of economies by the diversity of their non-ubiquitous products and
services. Economic complexity is indicative of countries economic growth,
income level, emissions and inequalities [21]. By now, the concept is applied
to different data sources such as patents, occupations or scientific
publications and to diverse spatial scales from countries to cities [6, 30].
Here we adopt the measurement technique to uncover the complexity of
neighborhoods and amenities. We propose that a neighborhood has a complex
amenity mix in case it offers diverse set of amenities of those types that
other locations are not specialized in. On the contrary, complex amenities are
those that only few neighborhoods are specialized into and are co-located with
diverse sets of similarly non-ubiquitous amenities. Unlike in the original
framework of economic complexity that captures the knowledge and capabilities
required to achieve economic outputs [23], our approach does not address the
productive and operative knowledge that a given location has accumulated [21].
Instead, we measure the sophistication of local amenity supply that can serve
a wide range of unique needs.

The rational to apply neighborhood and amenity complexity to understand mixing
of people is based on two reasons. First, diverse amenity mixes in
neighborhoods can attract people with diverse demands. Second, locations with
non-ubiquitous amenities can attract people from diverse neighborhoods, as the
particular service is hard to find elsewhere. Consequently, complex amenities
combining diversity and non-ubiquity are also expected to attract diverse
visitors. Therefore, our hypothesis is that the diverse mix of non-ubiquitous
amenities can create an inclusive, multipurpose neighborhood that is most
likely to be attractive for a wide-variety of people. While the contribution
of amenity mix to the socio-economic diversity of visitors at urban locations
has rarely been unveiled, diverse amenities are argued to concentrate in and
attract people to central places of cities [49]. To better understand the
connection between neighborhood and amenity complexity, urban centrality and
socio-economic mixing, we test their correlation with the socio-economic
diversity of visitors.

We test this argument in Budapest, the capital of Hungary by combining point
of interests (POI) data collected from the Google Places API and individual
mobility trajectories collected by a GPS aggregator company. Building on the
work of [22], we construct the indicators of neighborhood and amenity
complexity by utilizing the geographic distribution of POIs in neighborhoods.
We identify home, work and third place visits in daily mobility trajectories
for 24 months by clustering the geolocated pings of devices in geographical
space and over time [37]. We combine the information of predicted home
locations with real estate prices at the census tract level. This allows us to
investigate third place visits and to infer the socio-economic diversity of
visitors in each urban neighborhood and in each actual amenity.

Our results illustrate that, in the monocentric city of Budapest,
specialization and diversity of amenities do not, but amenity complexity is
correlated with urban centrality. We find that socio-economic mixing increases
as neighborhood complexity grows, and that amenity complexity is also
associated with lower levels of experienced segregation. These suggest that
the combination of mobility data with economic complexity thinking can provide
new insights to the research of urban segregation and mixing.

##  2 Tracing mobility inside cities

Urban mobility of individuals are studied by using raw GPS data from a data
aggregator company. We can trace the daily mobility of 5.2 million devices in
Hungary over 24 months (between 2019 June and 2021 May). We initially filter
this data to focus on devices that appear inside Budapest and have at least 20
GPS pings in total after discarding pings which indicate unreasonably high
speeds of device mobility. Detailed description on the mobility data
preparation process can be found in section 1 of the Supplementary
information.

Figure 1: Identifying home locations and third places visits from daily
mobility trajectories. (A) Example trajectory to illustrate the stop detection
process. (B) Identified stops and predicted home, work, and visited third
places. (C) Average number of home location and (D) average number of third
place visits over 24 months by urban neighborhoods of Budapest. (E) The
relationship between average number of home locations over 24 months and
population of urban neighborhoods in Budapest. (F) Real estate prices at
census tracts of identified home locations and across all census tracts of
Budapest.

We process raw trajectories of individuals by applying the Infostop algorithm
[4]. It enables us to detect the stationary points of individual movements and
cluster GPS pings around stop locations. Figure 1A-B illustrates the raw data
and the outcome of stop detection through an example device. The algorithm
gives each stop a label indicating a place that can reoccur along the
trajectory of the device. We focus on devices with at least 2 distinct places
and 10 stops in a month inside Budapest. Using the monthly recurrence of stops
and places by each device, we label places as home, work or third place visits
in two steps.

First, we categorize each visited place as potential home or work based on the
part of the day it is visited, the duration of visits and their reappearance
in the daily trajectory. The potential home is where the device spends the
most time between 8:00pm and 8:00am on weekdays or at any time during the
weekend, and the cumulative time spent at the place exceeds 8 hours per week.
Places where devices spend the most time between 9:00am and 5:00pm on weekdays
(at least 3 hours a week) are considered as potential workplaces.

Second, we time-aggregate device trajectories to monthly visitation patterns.
Thus, we identify home and work of a device in a month by the mean coordinate
pairs of weekly potential home and work places, but only in case a device
stops at the place at least 10 times over a month and the standard deviation
of both latitude and longitude coordinates are smaller than 0.001 (about 100
meters in Budapest) over the respective month. We categorize every other
visited place as a third place, in case it is labeled by the stop detection
algorithm as a unique place, but it is not the home or the work place of the
device in the respective month. Figure 1C presents the average number of
devices with identified home location (and at least one visited third place)
and Figure 1D illustrates the average number of third place visits over the
24-month period aggregated to the level of urban neighborhoods.

Home locations and third places are joined to other data sources with Uber’s
Hexagonal Hierarchical Spatial Index (H3) [46]. The applied indexes of size 10
H3 hexagons refer to an average 15.000 m2 area, which is close to the buffer
area of a point with a 70 meter radius. We connect all the identified home
locations and third places to hexagons and split each neighborhood or census
tract level polygons to the same hexagon size for efficient combination.

To infer the socio-economic status of the followed devices, we join home
locations to census tract level real estate prices. In Hungary, information on
income is not part of the census data collection. We rely on residential real
estate sales contracts from 2013-2019 collected by the Hungarian Central
Statistical Office and predict real estate prices to each census tract of
Budapest. Section 2 in the Supplementary information introduces the prediction
process in detail. Figure 1F presents that real estate prices at the
identified home locations and across all census tracts are closely align.

##  3 Measuring amenity complexity

To describe the attractiveness of urban locations, we construct the measures
of amenity complexity. These indicators are based on the spatial distribution
of amenities, which is studied through point of interest (POI) data from the
Google Places API. Besides its limitations in terms of timescale and POI
categorization, it is one of the world’s most popular mapping service
supporting applications worldwide and helping millions of individuals on a
daily basis to find the location of businesses. This makes Google data
attractive to study the spatial organization of amenities inside cities [22,
27, 20].

We collected GPS coordinates and amenity category for all the POIs around the
city of Budapest in early 2022. The resulted data set contains 63.601 POIs in
78 different amenity categories. We removed the frequently appearing and
ambiguous categories of ATM (1.054 POIs) and Parking (729 POIs) and filter out
the category Casino with less than 2 POIs in Budapest. We use this data to
illustrate the amenity profile of the 207 urban neighborhoods of Budapest
[25]. Neighborhoods are in between districts and census tracts in the spatial
hierarchy, which makes them a suitable scale for our analysis [35]. They have
an average population of 10.000 people (standard deviation around 10.000),
have an average area of 2.5 km2 (standard deviation around 3.9) and on average
they consist of 41 lower level census tracts (standard deviation around 50).
Further description about the neighborhoods of Budapest can be found in
section 3 of the Supplementary information.

Every neighborhood in Budapest with at least 2 amenity categories that have
minimum 2 POIs are considered in the analysis. Alternative specifications and
their influence on amenity complexity measurement can be found in section 4 of
the Supplementary Information. Figure 2A presents the resulted 75 amenity
categories and the number of POIs across the focal 200 neighborhoods. The most
frequent categories are convenient store (5.989 observations), beauty salon
(4.461 observations) and restaurant (3.727 observations), while we observe
less than 10 amusement parks, bowling alley and city hall. Figure 2B
illustrates the unequal spatial distribution of POIs on the map of
neighborhoods in Budapest.

Figure 2: Constructing the measures of neighborhood and amenity complexity.
(A) Distribution of point of interests (POIs) across neighborhoods and amenity
categories. (B) Map of urban neighborhoods colored by the number of observed
POIs. (C) Revealed comparative advantage (RCA) values transformed to a binary
specialization matrix (M). (D) Similarity matrix of neighborhoods based on
their specialization in amenity categories. This matrix is used to measure
neighborhood complexity. (E) Similarity matrix of amenities based on their
specialization in neighborhoods. This matrix is used to measure amenity
complexity. (F) Relationship between amenity diversity and average amenity
ubiquity in neighborhoods. Dots (neighborhoods) are colored by their
neighborhood complexity value. (G) Relationship between ubiquity and average
diversity of amenities. Dots (amenity categories) are colored by their amenity
complexity value. (H) Neighborhoods with higher complexity value are
specialized in amenity categories that have a higher amenity complexity value.
Each cell in the matrix represents a neighborhood specialized in an amenity
category and cells are colored by amenity complexity.

To describe the relative importance of amenity categories and illustrate the
differences between the amenity structure of neighborhoods, we adopt the
economic complexity index (ECI) and the product complexity index (PCI) [23].
The ECI is successfully used to describe the economic development of countries
and regions [21] and its approach is adoptable to amenities and urban
neighborhoods. We measure neighborhood complexity and amenity complexity the
following way. We normalize the matrix of Figure 2A to make comparisons
appropriate between neighborhoods and amenity categories and compute the
revealed comparative advantage (RCA) of neighborhoods in amenity categories by
the following standard equation (also known as the Balassa index):

$RCA_{n,a}=(P_{n,a}/P_{a})/(P_{n}/P)$ (1)

where $P_{n,a}$ is the number of POIs in neighborhood $n$ in amenity category
$a$ and missing indices indicate summed variables such as
$P_{a}=\sum_{a}P_{n,a}$. RCA $>=$ 1 suggests that neighborhood $n$ is
specialized in amenity category $a$. In other words, an amenity category is
overrepresented in a neighborhood in case its RCA value is above or equal to
1. We use the $RCA$ values to create a binary specialization matrix $M_{n,a}$
the following way:

$M_{n,a}=\left\\{\begin{array}[]{ccl}1&\textrm{if}&RCA_{n,a}>=1\\\
0&\textrm{if}&RCA_{n,a}<1\end{array}\right.$ (2)

Figure 2C illustrates the resulted binary $RCA$ matrix of neighborhoods and
amenity categories in Budapest. Sum of rows in this matrix presents the number
of amenity categories a neighborhood has comparative advantage in (amenity
diversity) and the column sums give the number of neighborhoods where an
amenity category is overrepresented (amenity ubiquity).

$\textrm{Amenity diversity}=M_{n}=\sum_{a}M_{n,a}$ (3)

$\textrm{Amenity ubiquity}=M_{a}=\sum_{n}M_{n,a}$ (4)

In geographic matrices like $M$ the average ubiquity of the activities present
in a location tends to correlate negatively with the diversity of activities
in a location. This is the result of the matrix property known as nestedness
and this feature is utilized to explain that more complex activities are only
available at a handful of locations with a diverse portfolio of activities
[23, 7].

$\textrm{Neighborhood complexity}=K_{n}=\frac{1}{M_{n}}\sum_{a}M_{n,a}K_{a}$
(5)

$\textrm{Amenity complexity}=K_{a}=\frac{1}{M_{a}}\sum_{n}M_{n,a}K_{n}$ (6)

The economic complexity index (ECI) that describes the production structure of
economies and the product complexity index (PCI) that describe the complexity
of products were originally defined through the iterative, self-referential
algorithm of the ’method of reflection’ [23]. The algorithm calculates the
above explained diversity and ubiquity vectors and then recursively uses the
information in one equation to correct the other (see 5) and (6). Later it was
presented that the method of reflection is equivalent to finding the
eigenvectors of the similarity matrix $M_{nn^{\prime}}$ and $M_{aa^{\prime}}$
[32, 21]. In our case $M_{nn^{\prime}}$ is defined from the original binary
neighborhood-amenity matrix $M$ as $M_{nn^{\prime}}=M^{T}*M$. The
neighborhood-neighborhood similarity matrix used to construct our neighborhood
complexity measure is visualized by Figure 2D. Neighborhood complexity is
analogous to economic complexity in terms of measurement and it captures the
amenity complexity of neighborhoods. To measure the complexity of amenity
categories based on their geographic distribution across neighborhoods, we
create an amenity-amenity similarity matrix as $M_{aa^{\prime}}=M*M^{T}$,
visualized by Figure 2E. The network representation and the clustered version
of this matrix can be found in Section 5 in the Supplementary information. Our
amenity complexity measure is constructed in a similar way to the product
complexity index. As discussed in the Introduction, neighborhood complexity
and amenity complexity are interpreted as measures of the sophistication of
the local amenity supply that can serve a wide range of unique needs.

Applying the most common approach to measure complexity from geographical
matrices, we take the second eigenvector of $M_{nn^{\prime}}$, which is the
leading correction to the equilibrium distribution and is the vector that is
the best at dividing neighborhoods into groups based on the amenities that are
present in them. Similarly, we take the second eigenvector of
$M_{aa^{\prime}}$ to get the amenity complexity values of amenity categories.
This process to measure complexity is similar to dimension reduction
techniques (singular value decomposition) that provide ways to explain the
structure of matrices (for an overview, see [21]).

Figure 2F illustrates the relationship between amenity diversity and average
amenity ubiquity of neighborhoods. Each point represents a neighborhood and is
colored by the derived neighborhood complexity values. Besides the expected
negative correlation between amenity diversity and average amenity ubiquity
[21], neighborhood complexity and the diversity of amenities at these
locations shows remarkable variance. Figure 2G presents the relationship
between the ubiquity of amenity categories and their average diversity. Each
point stands for an amenity category and is colored by the derived amenity
complexity values. Overall, we observe that more complex amenity categories
are non-ubiquitous and on average appear in more diverse areas. However, the
figure indicates a clear outlier (bottom left corner), zoo, which is very non-
ubiquitous and at the same time appears in less diverse neighborhoods. Figure
2H visualizes the mechanical relationship between amenity complexity and
neighborhood complexity. The figure makes it clear that complex neighborhoods
have complex amenities. These patterns are in line with the ones revealed by
[32] for countries and exported products. Section 6 in the Supplementary
information presents the ranking of neighborhoods and amenities in Budapest by
their neighborhood complexity and amenity complexity values.

Figure 3: Components of neighborhood complexity and their relationship with
geographical centrality in Budapest. (A) Map of Budapest colored by the
amenity diversity, (B) by the average amenity ubiquity, (C) by the amenity
complexity of neighborhoods. (D) Relationship between the geographical
centrality and neighborhoods’ amenity diversity, (E) average amenity ubiquity,
(F) and neighborhood complexity.

Figure 3A, B and C presents amenity diversity, average amenity ubiquity and
neighborhood complexity on the map of Budapest, while Figure 3D, E and F
illustrates their correlation with the geographical centrality of
neighborhoods in the city. The geographical centrality of locations (both in
case of neighborhoods and actual amenities) is determined by the inverse of
the average distance to reach the centroid of the location (on a logarithmic
scale) from the center of every census tract in Budapest. Since census tracts
are relatively homogeneous in terms of population, but heterogeneous in their
area, this measure gives us higher values for more densely populated, central
locations around the historical city center. To facilitate interpretation, the
measure is normalized to a scale of 0-1. As this metric is not based on
heuristics or local knowledge, it can be applied to other cities and is
motivated by the approach taken by [33], who showed in detail that the average
travel distance to locations is related to the diversity of visitors. In
section 7 of the Supplementary information, we provide further details on our
measure of geographic centrality, compare our results with the use of several
other centrality metrics, and discuss their differences in terms of
expectations about their social mixing abilities. Figure 3 suggests that all
three variables correlate with central location, but the correlation is
stronger for the average amenity ubiquity (-0.538) and neighborhood complexity
(-0.464).

Figure 4: Components of amenity complexity and their association with
geographical centrality in Budapest. (A) Amenities colored by their average
amenity diversity, (B) by their amenity ubiquity, (C) and by their amenity
complexity in the map of the city center. (D) Relationship between the
geographical centrality of locations and average diversity, (E) ubiquity, and
(F) complexity of amenity categories. Each dot is an amenity category and
centrality of location is a category average.

Figures 4A, B and C illustrate actual amenities on a zoomed in map of inner
Budapest through size 10 H3 hexagons colored by the average diversity,
ubiquity and amenity complexity of amenity categories at the location. At
dense inner locations of the city, some hexagons contain amenities in multiple
amenity categories. The identification of the dominant amenity category is
detailed in section 8 of the Supplementary information. Figures 4D, E and F
show how average amenity diversity, amenity ubiquity and amenity complexity
are associated with central location. While average diversity and ubiquity of
amenities have no clear connection to urban centrality (correlations are 0.180
and -0.056), Figure 4F suggests that complex amenities tend to be located
around the city center (correlation is 0.451, with three remarkable outliers).

##  4 Results

###  4.1 Diversity of visitors to complex urban neighborhoods

To illustrate the properties of urban locations that attract people of diverse
socio-economic status, we combine our neighborhood complexity index with more
granular visitation patterns from mobility data. Figure 5 presents our process
to join data sources through the example neighborhood of Középső-Ferencváros.

Figure 5: Neighborhood complexity and visitors to an example neighborhood in
February 2020. (A) Selected urban neighborhood of Középső-Ferencváros. (B)
Home location of devices visiting Középső-Ferencváros. (C) Real estate prices
at the home location of visitors. (D) Distribution of neighborhood complexity
values. The red vertical line indicates the complexity of the selected
neighborhood of Középső-Ferencváros. (E) Distribution of observed visitors in
neighborhoods. The red vertical line indicates the number of visitors in the
selected neighborhood. (F) Distribution of real estate prices across all
census tracts and at the home census tracts of visitors to the selected
neighborhood.

Figure 5A presents the location of the selected neighborhood, while Figure 5B
visualizes the home location of devices that visited any third places in
Középső-Ferencváros during the month of February 2020. We connect the home
location of visitors to census tracts as Figure 5C illustrates. This allows us
to infer the socio-economic status of visitors reflected by the real estate
prices at the census tract of their home location. Figure 5D shows that the
amenity mix at the selected neighborhood is relatively complex, while Figure
5E and F show that Középső-Ferencváros is visited by more devices than most
neighborhoods in February 2020 and its visitors come from diverse census
tracts from all around Budapest.

Table 1: Controlled correlations between the socio-economic diversity of visitors and the amenity complexity of neighborhoods | Coefficient of variation
---|---
| (1) | (2) | (3) | (4) | (5)
Neighborhood complexity |  | 0.125∗∗∗ |  |  | 0.125∗∗∗
|  | (0.036) |  |  | (0.038)
Amenity diversity |  |  |  $-$0.148∗ |  |  $-$0.162∗∗
|  |  | (0.076) |  | (0.074)
Avg amenity ubiquity |  |  |  |  $-$0.049 |  $-$0.017
|  |  |  | (0.049) | (0.050)
Centrality of location | 0.130∗∗∗ | 0.089∗∗∗ | 0.129∗∗∗ | 0.123∗∗∗ | 0.087∗∗∗
| (0.027) | (0.028) | (0.026) | (0.027) | (0.028)
Population (log) |  $-$0.053∗∗ |  $-$0.050∗∗ |  $-$0.049∗∗ |  $-$0.047∗∗ |  $-$0.043∗
| (0.022) | (0.022) | (0.022) | (0.023) | (0.022)
Nr visitors (log) | 0.047 | 0.039 | 0.054∗ | 0.045 | 0.046
| (0.029) | (0.029) | (0.029) | (0.029) | (0.029)
Nr POIs (log) |  $-$0.001 | 0.006 | 0.047 |  $-$0.013 | 0.054
| (0.023) | (0.023) | (0.033) | (0.026) | (0.034)
Constant | 0.424∗∗∗ | 0.363∗∗∗ | 0.360∗∗∗ | 0.460∗∗∗ | 0.306∗∗∗
| (0.056) | (0.057) | (0.064) | (0.066) | (0.075)
Observations | 186 | 186 | 186 | 186 | 186
R2 | 0.257 | 0.303 | 0.273 | 0.261 | 0.321
Adjusted R2 | 0.241 | 0.284 | 0.253 | 0.241 | 0.295
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

To capture socio-economic mixing at urban locations, we measure the diversity
of visitors in each neighborhood for every month by calculating the
coefficient of variation (ratio of standard deviation to the mean) of the real
estate prices at the home census tracts of visitors. We focus only on
neighborhoods with at least 10 observed visitors in the focal month to get
meaningful measures. Table 1 presents controlled correlations testing the
relationship between the diversity of visitors and the amenity structure of
neighborhoods using simple OLS regressions on February 2020 data. Model (1) is
our baseline model that illustrates the relationship between the diversity of
visitors and the centrality of neighborhoods, while controlling for
population, number of visitors and number of POIs in neighborhoods. The
positive and significant coefficient for urban centrality suggests that
central neighborhoods that are on average less distant from the census tracts
of Budapest are visited by more diverse people. Model (2) builds on the same
model structure, but includes neighborhood complexity as an explanatory
variable. It suggests that neighborhood complexity has positive and
significant correlation with the diversity of visitors, while taking into
account, among other things, the urban centrality of neighborhoods.
Interestingly, the diversity of amenities shows a mere negative correlation,
while the average ubiquity of amenities is not correlated with socio-economic
diversity of visitors in our case (see models (3) and (4) in Table 1). Model
(5) includes all the key explanatory variables and highlight the stable,
significant connection between neighborhood complexity and the diversity of
visitors.

The average variance inflation factor (VIF) is below 10 in all of the above
models, and the VIFs of our main explanatory variables are below 2 in all
cases, indicating no serious problems of multicollinearity. In section 7 of
the Supplementary information, we illustrate the robustness of our results by
using a number of alternative measures of location centrality. Models using
centrality metrics based on local knowledge show slightly different results,
but for our main models in Table 1 we use the most general and adoptable
centrality measure. Using the Gini coefficient or the Theil index to capture
the diversity of visitors, we get the same results. Related model outputs can
be found in section 9 of the Supplementary information. We run the same models
presented in Table 1 on the visitation patterns of non-local users only and
observe similar results. In this setting we only consider users living outside
the focal neighborhood. Related models are presented in section 10 of the
Supplementary information.

Furthermore, the relationship between neighborhood complexity and socio-
economic diversity of visitors is estimated for each of the available 24
months using the setting of model (2) in Table 1. The related figure in
section 11 of the Supplementary information suggests that neighborhood
complexity has a positive and significant relationship with the diversity of
visitors to neighborhoods in 18 out of the available 24 months. The possible
reasons behind the uneven coefficients are discussed in section 5.

Both Figure 3 and Figure 4 suggest that our neighborhood and amenity
complexity measures are correlated to urban centrality. Indeed, neighborhood
complexity and amenity complexity are derived from the spatial distribution of
amenities and then used to explain visits to spatial units, which may raise
spatial autocorrelation and endogeneity problems [10, 41]. We address
potential endogeneity issues by applying two different instrumental variable
(IV) approaches. Results of IV regressions presented in section 12 of the
Supplementary information further strengthen our argument that neighborhood
complexity is connected to the socio-economic diversity of visitors.

###  4.2 Diversity of visitors to complex amenities

To go beyond the level of neighborhoods, we combine amenity complexity
measured at the amenity category level with visitations to actual amenities
derived from our fine-grained mobility data. Figure 6 presents our process to
join data sources at the level of amenities through an example bar in the
neighborhood of Középső-Ferencváros, Budapest. The selected amenity is
surrounded by other amenities (Figure 6A) and by detecting the home location
of visitor devices (in Figure 6B we use February 2020 data and the surrounding
area in size 10 H3 hexagons), we can observe the socio-economic status of
visitors proxied by real estate prices (Figure 6C). Our Bar example is a
relatively complex amenity category (Figure 6D) and is very frequently visited
in comparison to other observed amenities in February 2020 (Figure 6E). In
addition, visitors from census tracts with medium or higher real estate prices
are over-represented in February 2020, as shown in Figure 6F.

Figure 6:  Connecting amenity complexity to visitor diversity. (A) Selected
bar on a map. Light red color hexagons indicate other nearby amenities. (B)
Neighboring home location of visitors. (C) Real estate prices in the census
tract of the visitor home locations. (D) Distribution of amenity complexity
values. The red vertical line indicates the amenity complexity of bars, the
selected amenity category. (E) Distribution of visitors to observed amenities
in February 2020, Budapest. The red vertical line indicates the number of
visitors at the example bar. (F) Distribution of real estate prices in all
census tracts and in census tracts where the visitors of the example bar live.

We measure the socio-economic diversity of visitors to each amenity for every
month by calculating the coefficient of variation (ratio of standard deviation
to the mean) of the real estate prices at the home census tracts of visitors.
To do so, we focus only on amenities with at least 10 observed visitors in the
focal month that helps us avoid meaningless values of the indicator. Table 2
presents simple OLS models to illustrate the relationship between the socio-
economic diversity of visitors and components of amenity complexity at the
level of amenities in February 2020. All our models at the level of amenities
present clustered standard errors at the level of amenity categories.

We find in Model (1) that geographical centrality is a significant predictor
of socio-economic mixing at amenities, even after controlling for the total
number of POIs in the respective amenity category across Budapest and the
observed number of visitors to the amenity in the focal month. Model (2)
presents that amenity complexity has an additional positive and significant
relationship with the socio-economic mixing. The negative and significant
coefficient of amenity ubiquity in Model (3) suggests that amenities that many
urban locations are specialized in are visited by less diverse, while
amenities that only few neighborhoods specialized in are visited by more
diverse groups of people. This result is consistent with the findings of [33].
The positive and slightly significant coefficient on the average diversity of
amenities in Model (4) indicates that amenity categories that mostly appear in
diverse neighborhoods attract visitors with different socio-economic status.
Model (5) includes all the key explanatory variables and highlight the stable,
significant connection between amenity complexity and the diversity of
visitors. While the effect of amenity diversity remains stable, the
significance of average amenity diversity disappears in the final model.

Table 2: Controlled correlations between the socio-economic diversity of visitors and amenity complexity | Coefficient of variation
---|---
| (1) | (2) | (3) | (4) | (5)
Amenity complexity |  | 0.069∗∗∗ |  |  | 0.040∗∗∗
|  | (0.016) |  |  | (0.015)
Amenity ubiquity |  |  |  $-$0.071∗∗∗ |  |  $-$0.051∗∗
|  |  | (0.015) |  | (0.018)
Avg amenity diversity |  |  |  | 0.047∗∗ |  $-$0.007
|  |  |  | (0.024) | (0.018)
Centrality of location | 0.126∗∗∗ | 0.116∗∗∗ | 0.118∗∗∗ | 0.125∗∗∗ | 0.115∗∗∗
| (0.011) | (0.011) | (0.010) | (0.011) | (0.010)
Nr POIs in category (log) |  $-$0.013 |  $-$0.006 | 0.015∗ |  $-$0.001 | 0.009
| (0.009) | (0.007) | (0.009) | (0.009) | (0.008)
Nr visitors (log) | 0.073∗∗∗ | 0.069∗∗∗ | 0.068∗∗∗ | 0.071∗∗∗ | 0.067∗∗∗
| (0.007) | (0.008) | (0.008) | (0.007) | (0.008)
Constant | 0.220∗∗∗ | 0.172∗∗∗ | 0.180∗∗∗ | 0.173∗∗∗ | 0.170∗∗∗
| (0.033) | (0.030) | (0.027) | (0.036) | (0.028)
Observations | 2,742 | 2,742 | 2,742 | 2,742 | 2,742
R2 | 0.102 | 0.108 | 0.108 | 0.104 | 0.110
Adjusted R2 | 0.101 | 0.106 | 0.107 | 0.102 | 0.108
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
| Standard errors are clustered at the amenity category level.

The average VIF value is below 3 in all of the above models, and the VIFs of
our main explanatory variables are close 1 in all cases, indicating no serious
problems of multicollinearity. Results with alternative measures for location
centrality can be found in section 7 of the Supplementary information. Amenity
complexity is significantly related to socio-economic mixing using almost any
centrality indicators. Changing the dependent variable to the Gini coefficient
or the Theil index to capture the diversity of visitors to amenities, we
obtain the same results. Related model outputs can be found in section 9 of
the Supplementary information. The relationship between amenity complexity and
socio-economic diversity of visitors is estimated for each of the available 24
months using the setting of model (2) in Table 2. The related figure in
section 11 in the Supplementary information presents that amenity complexity
has a positive and significant relationship with the diversity of visitors to
amenities in 16 out of the available 24 months.

##  5 Discussion

In this work we bring the ideas behind economic complexity metrics to the
urban problems of experienced segregation and social mixing. We measure
amenity complexity by utilizing the spatial distribution of point of interests
(POIs) inside a city. We combine the information on the complexity of
neighborhoods and of amenity categories with fine-grained mobility data to
illustrate the relationship between the complexity of amenities available in a
location and the socio-economic diversity of its visitors. Focusing on the
urban neighborhoods of Budapest, Hungary, we find that neighborhoods that
concentrate a more complex amenity mix attract a bigger diversity of socio-
economic groups. Applying the same logic to actual amenities inside Budapest,
we also show that POIs of more complex amenity categories are visited by
larger diversities of strata. However, the diversity and ubiquity of
amenities, the two components of amenity complexity, show a less clear
relationship with the socio-economic diversity of visitors. Diversity of
amenities shows a surprising negative correlation with visitor diversity, but
only at the neighborhood level, while ubiquity of amenities is related to
visitor diversity only at the amenity category level.

The geographical centrality of urban locations is a strong predictor of socio-
economic mixing. Our results illustrate that both neighborhood complexity and
amenity complexity correlate with the geographical centrality of locations.
Contrary to previous works [49], we find that diversity of amenities is less
correlated to urban centrality, while amenity ubiquity is only associated with
centrality of locations at the neighborhood level. The relationship between
amenity complexity and centrality of locations has inspired a number of
robustness checks, including the use of instrumental variable regressions
(details can be found in section 7 and section 12 of the Supplementary
information), which further confirm our key finding that amenity complexity is
associated with socio-economic diversity of visitors.

The general contribution of our paper is that we combine economic complexity
concepts with urban mobility research. Constructing the measures of
neighborhood and amenity complexity allows us to systematically test the
contribution of certain amenity categories and also the amenity portfolio at
certain locations to socio-economic mixing in cities. Moreover, we contribute
to the line of research on segregation patterns inside cities by illustrating
in a direct fashion based on fine-grained mobility data that centrality of
urban locations largely influence socio-economic mixing.

Our empirical work has several limitations, but offers promising future
research directions. This study only focuses on the city of Budapest. Budapest
is the only large city in Hungary and it clearly has a monocentric structure.
Therefore, our findings are limited to this specific context and similar
empirical works in cities with different size, geography and urban structure
are necessary to assess the generality of our conclusions.

To construct the amenity complexity measures, we rely on the specific
neighborhood structure of Budapest, however, alternative spatial scales in
different urban settings are necessary to be tested in the future. We believe
that the level of neighborhoods is the appropriate spatial scale to construct
amenity complexity metrics for two reasons. First, the size of the applied
spatial units can influence the nestedness of the location-amenity matrix used
to construct complexity metrics. Co-occurrence of POIs in different amenity
categories are less likely in case we consider smaller geographical areas.
Neighborhoods are proved to be large enough to produce intuitive results.
Second, neighborhoods are very important spatial units of urban life. They are
argued to be the environment that can influence social capital accumulation
and social mobility [13, 12]. Moreover, they have clear administrative
boarders and people can identify with them, which makes the interpretation of
amenity complexity results more appealing.

Inside Budapest, we observe that central location is correlated to both
neighborhood complexity and amenity complexity and these factors are all
connected to the socio-economic diversity of visitors. To understand this
relationship clearly, we test several different measures of central location,
with mixed results. For our main empirical exercise we choose the centrality
metric based on the average distance to reach neighborhoods and amenities from
any census tracts inspired by [33], as this measure does not require local
knowledge and is easy to adopt for other cities. However, further research is
needed to better understand these relationships, as a recent work based on
similar measures adopted to Paris, France, shows that amenity complexity is
not exclusively linked to a single city center [40].

Mobility data for our empirical analysis are produced on a monthly basis. Our
findings are valid for 16 of the 24 months available and COVID-19 did not
clearly affect the relationship between amenity complexity and the diversity
of visitors to urban locations. However, our data does not contain enough
observations to provide significant results for all the 24 months under study.
Confirming the results with better mobility data is an important future
research direction.

The counting of POIs within neighborhoods does not allow differentiation
between the capacity or quality of amenities. We have tested unsuccessfully
the number of visitors to amenity categories within neighborhoods as an input
rather than the sheer number of POIs. In the future, similar but more
sophisticated data would be needed to measure amenity complexity more
accurately.

In our empirical exercise, we adopted the most commonly used economic
complexity indicator to amenities and neighborhoods. However, several
modifications have been suggested to improve economic complexity measurement
[44, 32] and the adoption of these methods to the neighborhood scale in urban
environments is an apparent future research direction.

## Acknowledgements

Sándor Juhász worked on the paper as a Marie Skłodowska-Curie Postdoctoral
Fellow at the Complexity Science Hub Vienna (grant number 101062606). The work
of Balázs Lengyel was financially supported by Hungarian National Scientific
Fund (OTKA K 138970). The authors acknowledge the help of Orsolya Vásárhelyi
and Luis Guillermo Natera Orozco with the original POI data collection. We
wish to thank Tom Broekel, Frank Neffke, Gergő Tóth and László Czaller for
their comments and suggestions. We acknowledge the significant assistance of
our illustrator Szabolcs Tóth-Zs. in finalizing our primary figures. The
authors thank the Social Science Computing Unit Budapest, and the Data Bank of
the Centre for Economic- and Regional Studies for the contribution in data
management.

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## Supplementary information

## S1 Mobility data preparation

Our GPS based mobility data is provided by a data aggregator company that
collects and combines anonymous location data from users’ smartphone
applications. The sample we use for our analysis is an unbalanced panel of GPS
pings from 5.2 million devices in Hungary between 2019 June and 2021 May. Our
raw data consists of a device identifier, a time stamp, a latitude, and a
longitude coordinate, where GPS pings occur. Pings are logged in case an
application on a device requests location information. Sometimes this is the
result of an active behavior such as using a navigation application or
requesting local weather information. In other cases, pings could be the
result of an application requesting information while running in the
background. As a consequence, pings occur at irregular intervals. To identify
visitation patterns such as home, work or third place visits to urban
locations, we transform and filter our raw GPS trajectory data in several
steps. We detail these steps in the following.

As the data contains some pings attributed to the same device that indicate
unreasonable behavior, we start by iteratively removing all ping pairs that
signal a movement over 300 kilometers per hour speed. Additionally, we discard
all devices that have fewer than 20 pings remaining after this initial speed-
based filter. These two steps reduce the total ping count from 3.18 billion to
3.13 billion and the total unique device count from 5.2 million to 1.88
million.

To focus on locations where devices stopped for some time, we run the Infostop
stop detection algorithm ([4]). In short, it classifies GPS pings to trips or
stays and clusters stationary points into stops in an effective way. We apply
the algorithm with the following parameter set. $r1$, the maximum roaming
distance allowed for two pings within the same stay is set to 370 meters.
$r2$, the typical distance between two stays in the same destination is set to
140 meters. $t_{min}$, the minimum duration of a stay is set to 270 seconds,
while $t_{max}$, the maximum time difference between two consecutive pings to
be considered within the same stay is set to 7200 seconds. The minimum number
of GPS pings required for stationary points is set to 2.

The parameters are calibrated using the Google location history data of 7
consenting individuals from Budapest, Hungary. We ran our stop detection
algorithm on the sample trajectories with a wide range of parameters. We
compared the results of the stop detection process to the personal, anecdotal
experiences and to the semantic stop detection extracted from Google accounts.
This experiment confirmed that the stop detection algorithm and the parameters
produce a reasonable set of trips, stays, and destinations. Moreover, the
subsequent home and work detection process built on it produced accurate
results for our small sample.

Using the output of the stop detection process, we further filter the data to
devices that have at least 2 unique destinations with over 4 different stays
in each. This reduces the total stop count from 100 million to about 80
million, and the unique device count from 1.75 million to about 240.000.
However, even in this final form, over 2.1 billion pings are used from the
original 3.18 billion. Our empirical exercise in the end only uses information
for each month from devices with identified home, work and at least a single
visited third place inside Budapest.

## S2 Socio-economic status from census tract level real estate prices

We infer on the socio-economic status of individuals living in Budapest by
connecting their identified home location to residential real estate prices at
the census tract level. Approximating socio-economic status through real
estate prices has several benefits in comparison to the prevalent solution of
using household income statistics of urban locations. First, real estate
prices are by definition connected to places, while it is harder to connect
income to locations. Second, real estate statistics in the census are
comprehensive, while income information only reflects on the status of active
employees.

The Hungarian Central Statistical Office collects data on all residential real
estate sales contracts and derives information on transaction prices for the
entire country. As not every real estate is on the market and observed
contracts sometimes suffer from missing information on the parameters of given
properties, direct measurement on lower geographical level is difficult. By
utilizing the fact that real estate prices tend to follow a strong multi-level
hierarchy as location (and especially neighborhoods in Budapest) explains much
of the price differences, we train a multi-level random slope regression model
on the observed transaction prices [14, 42]. To do so, we use real estate
transaction contracts between 2013 and 2019. We create a pooled setting by
correcting prices through the city level house price index published yearly by
the National Bank of Hungary. Our model can be written as:

$\begin{split}h_{i,j}=\beta_{0,j}+\beta_{1,j}s_{i,j}+\varepsilon_{i,j}\\\
\beta_{0,j}=\beta_{0}+n_{0,j}\\\ \beta_{1,j}=\beta_{1}+n_{1,j}\end{split}$ (7)

Here $h_{i,j}$ is the logarithm of the individual price of real estate $i$ in
neighborhood $j$. $\beta_{0,j}$ represents how much the estimated mean house
price differs by neighborhoods. Estimated mean neighborhood prices are
decomposed to $\beta_{0}$, the city level mean, and $n_{0,j}$, the
neighborhood deviation from this value. To be able to capture differences
within neighborhoods, we apply the individual level parameter $s_{i,j}$ that
refers to the size (floor area) of real estate $i$ in neighborhood $j$. Since
the effect of floor area can vary between neighborhoods, we train a random
slope model. $\beta_{1,j}$ represents the effect of floor area in neighborhood
$j$. $\beta_{1,j}$ is decomposed to a city level slope $\beta_{1}$, and the
deviation of neighborhood slopes around this value $n_{1,j}$.

Utilizing this model, we predict prices for every real estate captured by the
last Hungarian census in 2010. By taking the mean of the predicted real estate
prices at the census tract level, we get a highly granular socio-economic
status map for the entire city of Budapest. Figure 7A illustrates the
predicted prices aggregated to the census tract level on the map of Budapest,
while Figure 7B shows the distribution of predicted real estate prices.

Figure 7: Predicted real estate prices at the census tract level around
Budapest (A) and the distribution of real estate prices aggregated to the
census tract level in Budapest (B)

## S3 Urban neighborhoods of Budapest, Hungary

We use urban neighborhoods as geographic units to construct our amenity
complexity measures. Budapest consists of 207 urban neighborhoods and their
place in the spatial scale hierarchy is between districts and census tracts in
terms of area and population. The unequal size distribution of urban
neighborhoods are illustrated in Figure 8 and Figure 9. The correlation
between population of urban neighborhoods and the number of census tracts per
urban neighborhoods is strong as Pearson’s R is $0.979$. Further details about
neighborhoods can be found at the website of [25].

Figure 8: Population of urban neighborhoods based on the census of 2010 on the
map of Budapest (A) and as a distribution plot (B). Figure 9: Number of census
tracts per urban neighborhood based on the census of 2010 on the map of
Budapest (A) and as a distribution plot(B).

## S4 Alternative specifications to construct amenity complexity measures

To construct our amenity complexity measures, we create a neighborhood-amenity
category matrix, where we consider every neighborhood in Budapest with at
least 2 amenity categories with minimum 2 POIs. The minimum 2 POIs threshold
is implemented to reduce noise in our data. We use this matrix to measure the
revealed comparative advantage (RCA) of neighborhoods in amenity categories
and transform it to a binary specialization matrix ($M$) for the calculation
of complexity values at the level of neighborhoods and amenity categories, as
described in the main text. Figure 10 presents how the composition of $M$
would change in case we use alternative thresholds for minimum number of POIs
per amenity categories in neighborhoods.

Figure 10: Stability of RCA values in the binary specialization matrix ($M$) by different specifications. (A) Changes in RCA 0/1 values in case we consider every amenity category in each neighborhood with at least 1 POI. (B) Changes in RCA 0/1 values in case we increase the minimum number of POIs per amenity category in neighborhoods from 2 to 3. (C) Changes in RCA 0/1 values in case we increase the minimum number of POIs per amenity category in neighborhoods from 2 to 5. Figure 11: Correlation tables for (A) neighborhood complexity and (B) amenity complexity values created by applying different minimum thresholds on the number of POIs in the neighborhood-amenity category matrix. Table 3: Controlled correlations between the diversity of visitors and the complexity of neighborhoods (in February 2020) in cases we apply different minimum thresholds for the number of POIs considered in the neighborhood-amenity category matrix. | Coefficient of variation
---|---
| (1) | (2) | (3)
Neighborhood complexity | 0.125∗∗∗ |  |
| (0.036) |  |
Neighborhood complexity min 3 POIs |  | 0.133∗∗∗ |
|  | (0.045) |
Neighborhood complexity min 5 POIs |  |  | 0.098∗∗
|  |  | (0.039)
Centrality of location | 0.089∗∗∗ | 0.102∗∗∗ | 0.117∗∗∗
| (0.028) | (0.028) | (0.027)
Population (log) |  $-$0.050∗∗ |  $-$0.031 |  $-$0.021
| (0.022) | (0.023) | (0.023)
Nr visitors (log) | 0.039 | 0.037 | 0.040
| (0.029) | (0.029) | (0.029)
Nr POIs (log) | 0.006 |  $-$0.039 |  $-$0.052∗
| (0.023) | (0.025) | (0.028)
Constant | 0.363∗∗∗ | 0.394∗∗∗ | 0.396∗∗∗
| (0.057) | (0.055) | (0.055)
Observations | 186 | 184 | 177
R2 | 0.303 | 0.275 | 0.255
Adjusted R2 | 0.284 | 0.255 | 0.233
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 4: Controlled correlations between the diversity of visitors and the complexity of amenities (in February 2020) in cases we apply different minimum thresholds for the number of POIs considered in the neighborhood-amenity category matrix. | Coefficient of variation
---|---
| (1) | (2) | (3)
Amenity complexity | 0.069∗∗∗ |  |
| (0.016) |  |
Amenity complexity min 3 POIs |  | 0.077∗∗∗ |
|  | (0.020) |
Amenity complexity min 5 POIs |  |  | 0.094∗∗∗
|  |  | (0.030)
Centrality of location | 0.116∗∗∗ | 0.118∗∗∗ | 0.116∗∗∗
| (0.011) | (0.011) | (0.011)
Nr POIs in category (log) |  $-$0.006 | 0.012 | 0.022∗
| (0.007) | (0.009) | (0.012)
Nr visitors (log) | 0.069∗∗∗ | 0.067∗∗∗ | 0.067∗∗∗
| (0.008) | (0.008) | (0.008)
Constant | 0.172∗∗∗ | 0.121∗∗∗ | 0.094∗∗
| (0.030) | (0.036) | (0.045)
Observations | 2,742 | 2,740 | 2,739
R2 | 0.108 | 0.107 | 0.108
Adjusted R2 | 0.106 | 0.106 | 0.106
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Despite the different thresholds, around 90% of the neighborhood-amenity
category matrix is classified by the same 0/1 RCA value. This suggests that
matrix $M$ is relative stable for smaller changes in the minimum number of
POIs considered. In case we do not introduce any threshold to construct the
matrix $M$, we classify slightly more neighborhood-amenity category with
RCA=1.

Figure 11 presents the correlation tables for neighborhood and amenity
complexity values based on different minimum thresholds on the number of POIs.
The tables suggest that there is a clear difference in complexity values in
case we introduce a minimum threshold and in case we do not. Without any noise
filtering the resulted complexity values have a negative correlation to
complexity values constructed from neighborhood-amenity pairs with at least 2
POIs. We opt to choose the minimum 2 POIs threshold as it results in intuitive
complexity values for both neighborhoods and amenity categories, but still not
too restrictive. Table 3 and Table 4 presents that our main results are not
influenced by increasing the minimum 2 POIs threshold to minimum 3 or 5 POIs.

As an alternative specification, we constructed neighborhood and amenity
complexity measures based only on POIs that attract visitors along the 24
month long observed period. Figure 12 illustrates the stability of RCA 0/1
values in case we only consider POIs around Budapest visited by at least 1 or
at least 10 devices during the 24 months. The figure suggests that 94% of all
neighborhood-amenity pairs are classified by the same RCA value even in case
we consider the attraction of POIs at the beginning of the complexity measure
generation. Changing from 1 to 10 minimum visitor devices to POIs does not
change the classification results. Figure 13 presents strong correlations
between neighborhood and amenity complexity values based on the different
settings. Table 5 and Table 6 presents that our main results remain the same
even in case we build our complexity measures on POIs that actually attract
visitors.

Figure 12: Stability of RCA values in the binary specialization matrix ($M$) in case we only consider POIs (A) visited by at least 1 device, (B) visited by at least 10 devices during the observed 24 months. Figure 13: Correlation tables for (A) neighborhood complexity and (B) amenity complexity values created from the neighborhood-amenity category matrix where all POIs, visited POIs or POIs with at least 10 visitor devices during the observed 24 months are considered. Table 5: Controlled correlations between the diversity of visitors and the complexity of neighborhoods (in 2020 February) in case we consider POIs with visitors for the neighborhood complexity measurement. | Coefficient of variation
---|---
| (1) | (2) | (3)
Neighborhood complexity | 0.125∗∗∗ |  |
| (0.036) |  |
Neighborhood complexity visited POIs |  | 0.102∗∗∗ |
|  | (0.039) |
Neighborhood complexity POIs with min 10 visitors |  |  | 0.101∗∗
|  |  | (0.041)
Centrality of location | 0.089∗∗∗ | 0.107∗∗∗ | 0.107∗∗∗
| (0.028) | (0.028) | (0.028)
Population (log) |  $-$0.050∗∗ |  $-$0.044∗ |  $-$0.039
| (0.022) | (0.023) | (0.024)
Nr visitors (log) | 0.039 | 0.026 | 0.029
| (0.029) | (0.030) | (0.030)
Nr POIs (log) | 0.006 | 0.006 |  $-$0.007
| (0.023) | (0.023) | (0.023)
Constant | 0.363∗∗∗ | 0.380∗∗∗ | 0.379∗∗∗
| (0.057) | (0.059) | (0.059)
Observations | 186 | 182 | 181
R2 | 0.303 | 0.281 | 0.267
Adjusted R2 | 0.284 | 0.261 | 0.247
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 6: Controlled correlations between the diversity of visitors and the complexity of amenities (in 2020 February) in case we consider POIs with visitors for the amenity complexity measurement. | Coefficient of variation
---|---
| (1) | (2) | (3)
Amenity complexity | 0.069∗∗∗ |  |
| (0.016) |  |
Amenity complexity visited POIs |  | 0.075∗∗∗ |
|  | (0.017) |
Amenity complexity POIs with min 10 visitors |  |  | 0.075∗∗∗
|  |  | (0.018)
Centrality of location | 0.116∗∗∗ | 0.115∗∗∗ | 0.115∗∗∗
| (0.011) | (0.011) | (0.011)
Population (log) |  $-$0.006 | 0.001 | 0.004
| (0.007) | (0.007) | (0.008)
Nr visitors (log) | 0.069∗∗∗ | 0.069∗∗∗ | 0.070∗∗∗
| (0.008) | (0.007) | (0.007)
Nr POIs (log) | 0.172∗∗∗ | 0.154∗∗∗ | 0.148∗∗∗
| (0.030) | (0.030) | (0.031)
Observations | 2,742 | 2,742 | 2,742
R2 | 0.108 | 0.108 | 0.108
Adjusted R2 | 0.106 | 0.106 | 0.106
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

## S5 Similarity of amenities based on their co-location

Figure 14 presents an alternative, clustered version of the $M_{aa^{\prime}}$
amenity-amenity similarity matrix, which we use to construct our amenity
complexity measure. The strongest stand-alone clusters consist of ubiquitous
amenities such as Grocery or supermarket and Convenience store, which co-occur
in many neighborhoods with a concentration of $RCA>=1$. A normalized version
of this matrix is often represented as a network, similarly to the product
space or the knowledge space [21]. Figure 15 illustrates our amenity-amenity
similarity matrix as a network with non-normalized edge weights.

Figure 14: Clustered version of the amenity-amenity similarity matrix
$M_{aa^{\prime}}$. Colors of the matrix indicate the number of neighborhoods
we observe two amenity categories with RCA value above 1. Figure 15: Network
representation of the amenity-amenity similarity matrix $M_{aa^{\prime}}$.
Edges represent non-normalized values of co-concentration in neighborhoods.

## S6 Amenity complexity rankings

Ranking of all amenity categories (Figure 16) and all neighborhoods by their
amenity complexity values (Figure 17).

Figure 16: Amenity categories ranked by their amenity complexity value.
Categories are colored by their ubiquity across neighborhoods. Complexity and
ubiquity values are normalized to 0-1 scale for visualization purposes.

Figure 17: Neighborhoods of Budapest ranked by their amenity complexity value.
Neighborhoods are colored by the diversity of their amenities. Complexity and
diversity values are normalized to 0-1 scale for visualization purposes.

## S7 Centrality of locations in Budapest, Hungary

To identify central locations within the city of Budapest, we measure the
average distance of locations from each census tract of the city. More
precisely, for neighborhoods we measure the Euclidean distance between the
centroid of the focal neighborhood and the centroid of all census tracts and
calculate the average distance to reach the neighborhood from any census
tracts of the city. For actual amenities, we apply the same procedure and
calculate the average distance between the centroid of the focal H3 hexagon
and the centroid of all census tracts. For both neighborhoods and amenities,
we use the inverse of this average distance (log) normalized to 0-1 scale.
Figure 18 illustrates the resulted indicators on the map of Budapest, where
higher values are associated with locations around the historic inner city of
Pest. Figure 19 presents the distribution of the indicator for neighborhoods
and amenities.

Figure 18: Centrality of locations (A) Centrality of neighborhoods on the map
of Budapest, Hungary. Centrality is measured as the inverse of the average
distance to reach a neighborhood from all the census tracts of Budapest. (B)
Centrality of amenities on the map of Budapest, Hungary. Centrality is
measured by the inverse average distance to reach an amenity from all the
census tracts of Budapest. Areas in blue indicate natural water sources.
Figure 19: Distribution of centrality measures for (A) neighborhoods and (B)
amenities. Centrality of locations is defined as the inverse of the average
distance to reach the location from all the census tracts of Budapest. Areas
in blue indicate natural water sources.

We choose this solution to quantify the centrality of locations for several
reasons. First, Budapest has a convex shape and it is a clearly monocentric
city. The application of the Urban Centrality Index (UCI) proposed by [38] to
the population distribution between Budapest neighborhoods results in
Proximity Index (PI) of 0.999 and UCI of 0.386, indicating a highly
centralized structure. Second, we take advantage of the census tract
structure. Census tracts are relatively homogeneous in terms of population,
but very heterogeneous in terms of area. More specifically, census tracts tend
to be smaller around the city center and larger on the outskirts. The densely
populated inner city, which concentrates a large proportion of census tracts
results in many neighborhood-census tract pairs (and amenity-census tract
pairs) with shorter distances. As a result, the average value of distances
will be high for densely populated central locations. Third, this method
allows assigning a unique centrality value to each neighborhood and each H3
hexagon based on their relationship to the common spatial unit of the census
tracts. Finally, our metric is universal in the sense that it can be applied
to any city of similar shape and structure to identify the centrality of
locations, and is less city-specific than measuring the distance to an
arbitrary central location chosen based on local knowledge.

Table 7 shows how different measures on centrality of locations affect the
relationship between socio-economic diversity of visitors. The regressions are
based on the example month of February 2020, exactly like our models in the
main text. Model (1) is identical with our preferred model from the main text.
Model (2) tests the significance of the distance from the center of mass in
Budapest. Model (3) uses distance from the zero kilometer stone as an
alternative centrality measure. The zero kilometer stone (or landmark zero
sculpture) at Clark Ádám tér is the center of Hungary’s main road network, and
road network distances are calculated from here. Model (4) introduces the
distance from the center of Budapest defined by Deák Ferenc tér. This square
is a public transport hotspot in the heart of the city center. For model (5)
we compute the Local Indicator of Spatial Association (LISA) using the local
Moran’s I for the number of POIs per neighborhood [3]. More precisely, we find
the largest, statistically significant spatial cluster of neighborhoods in
which the number of POIs and the average number of POIs in its surroundings is
more similar than would be expected by pure chance [39]. The distance from
LISA center variable measures the distance of neighborhoods from the center of
the largest statistically significant spatial cluster. The resulting center is
near the Nyugati Railway Station, one of the largest railway stations in the
city. All the above variables capturing urban centrality are log transferred.
As all variables for urban centrality are significant and have the expected
sign (except the model using center of mass), Table 7 clearly illustrates that
urban centrality is related to socio-economic mixing.

Table 7: Controlled correlations between the socio-economic diversity of visitors and different measures on central location of neighborhoods | Coefficient of variation
---|---
| (1) | (2) | (3) | (4) | (5)
Centrality of location | 0.130∗∗∗ |  |  |  |
| (0.027) |  |  |  |
Distance from center of mass |  |  $-$0.015 |  |  |
|  | (0.025) |  |  |
Distance from zero km stone |  |  |  $-$0.151∗∗∗ |  |
|  |  | (0.019) |  |
Distance from Deak ter |  |  |  |  $-$0.151∗∗∗ |
|  |  |  | (0.022) |
Distance from LISA center |  |  |  |  |  $-$0.163∗∗∗
|  |  |  |  | (0.023)
Population (log) |  $-$0.053∗∗ |  $-$0.096∗∗∗ |  $-$0.040∗∗ |  $-$0.038∗ |  $-$0.038∗
| (0.022) | (0.023) | (0.020) | (0.021) | (0.021)
Nr visitors (log) | 0.047 | 0.099∗∗∗ | 0.036 | 0.034 | 0.024
| (0.029) | (0.029) | (0.026) | (0.027) | (0.027)
Nr POIs (log) |  $-$0.001 | 0.005 | 0.004 |  $-$0.0001 | 0.004
| (0.023) | (0.025) | (0.021) | (0.022) | (0.022)
Constant | 0.424∗∗∗ | 0.536∗∗∗ | 0.576∗∗∗ | 0.583∗∗∗ | 0.606∗∗∗
| (0.056) | (0.056) | (0.048) | (0.049) | (0.049)
Observations | 186 | 186 | 186 | 186 | 186
R2 | 0.257 | 0.162 | 0.376 | 0.335 | 0.350
Adjusted R2 | 0.241 | 0.144 | 0.363 | 0.321 | 0.336
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 8 presents how different measures on centrality of locations affect the
relationship between socio-economic diversity of visitors and neighborhood
complexity. Model (1) is used as a baseline, in which we do not control for
the centrality of neighborhoods at all. From model (2) to model (6), we
present one by one the measures of location centrality presented earlier. The
table shows mixed results. While the distance from the center of mass in
Budapest does not influence the diversity of visitors, the distance from
infrastructure hubs such as the zero kilometer stone, Deak tér or Nyugati
railway station, which is the result of the LISA calculation, have high
explanatory power.

Table 8: Controlled correlations between the socio-economic diversity of visitors, complexity of neighborhoods and alternative measures on central location | Coefficient of variation
---|---
| (1) | (2) | (3) | (4) | (5) | (6)
Neighborhood complexity | 0.172∗∗∗ | 0.125∗∗∗ | 0.172∗∗∗ | 0.028 | 0.056 | 0.042
| (0.034) | (0.036) | (0.034) | (0.040) | (0.041) | (0.041)
Centrality of location |  | 0.089∗∗∗ |  |  |  |
|  | (0.028) |  |  |  |
Distance from center of mass |  |  |  $-$0.005 |  |  |
|  |  | (0.024) |  |  |
Distance from zero km stone |  |  |  |  $-$0.140∗∗∗ |  |
|  |  |  | (0.025) |  |
Distance from Deak ter |  |  |  |  |  $-$0.127∗∗∗ |
|  |  |  |  | (0.028) |
Distance from LISA center |  |  |  |  |  |  $-$0.144∗∗∗
|  |  |  |  |  | (0.029)
Population (log) |  $-$0.075∗∗∗ |  $-$0.050∗∗ |  $-$0.074∗∗∗ |  $-$0.040∗∗ |  $-$0.040∗ |  $-$0.039∗
| (0.021) | (0.022) | (0.022) | (0.020) | (0.021) | (0.021)
Nr visitors (log) | 0.067∗∗ | 0.039 | 0.067∗∗ | 0.035 | 0.033 | 0.025
| (0.028) | (0.029) | (0.028) | (0.026) | (0.027) | (0.027)
Nr POIs (log) | 0.013 | 0.006 | 0.012 | 0.005 | 0.003 | 0.006
| (0.023) | (0.023) | (0.023) | (0.021) | (0.022) | (0.022)
Constant | 0.399∗∗∗ | 0.363∗∗∗ | 0.402∗∗∗ | 0.552∗∗∗ | 0.533∗∗∗ | 0.566∗∗∗
| (0.057) | (0.057) | (0.059) | (0.059) | (0.062) | (0.063)
Observations | 186 | 186 | 186 | 186 | 186 | 186
R2 | 0.265 | 0.303 | 0.266 | 0.378 | 0.342 | 0.354
Adjusted R2 | 0.249 | 0.284 | 0.245 | 0.361 | 0.324 | 0.336
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 9 and Table 10 apply the same logic and setting to amenities. Table 9
shows that measures of centrality of location work the same for amenities as
for neighborhoods, and that amenities in more central locations are visited by
socio-economically more diverse people. Table 10 presents models in which we
also control for amenity complexity. The results are mixed, and unlike at the
neighborhood level, amenity complexity is significant even after controlling
for distance from Deák tér or for the distance from the LISA center (Nyugati
railway station area). These regressions suggest that in addition to the
physical centrality of locations, centrality within the transport
infrastructure may also influence socio-economic mixing in Budapest, Hungary.
This would require further evaluation, as the zero kilometer stone, for
example, which has the largest explanatory power in both settings, is only a
symbolic center of the Hungarian road network. It does not serve as a meeting
point for the local population, nor can it be seen as a melting pot of
society. However, a deeper assessment is beyond the scope of this research.

Table 9: Controlled correlations between the socio-economic diversity of visitors and different measures on central location of amenities | Coefficient of variation
---|---
| (1) | (2) | (3) | (4) | (5)
Centrality of location | 0.126∗∗∗ |  |  |  |
| (0.011) |  |  |  |
Distance from center of mass |  |  $-$0.011 |  |  |
|  | (0.011) |  |  |
Distance from zero km stone |  |  |  $-$0.132∗∗∗ |  |
|  |  | (0.011) |  |
Distance from Deak ter |  |  |  |  $-$0.115∗∗∗ |
|  |  |  | (0.010) |
Distance from LISA center |  |  |  |  |  $-$0.109∗∗∗
|  |  |  |  | (0.012)
Nr POIs in category (log) |  $-$0.013 |  $-$0.021 |  $-$0.006 |  $-$0.006 |  $-$0.010
| (0.009) | (0.013) | (0.007) | (0.007) | (0.008)
Nr visitors (log) | 0.073∗∗∗ | 0.096∗∗∗ | 0.053∗∗∗ | 0.047∗∗∗ | 0.056∗∗∗
| (0.007) | (0.009) | (0.006) | (0.007) | (0.008)
Constant | 0.220∗∗∗ | 0.313∗∗∗ | 0.397∗∗∗ | 0.388∗∗∗ | 0.387∗∗∗
| (0.033) | (0.051) | (0.030) | (0.032) | (0.034)
Observations | 2,742 | 2,742 | 2,742 | 2,742 | 2,742
R2 | 0.102 | 0.052 | 0.167 | 0.143 | 0.138
Adjusted R2 | 0.101 | 0.051 | 0.166 | 0.142 | 0.137
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 10: Controlled correlations between the socio-economic diversity of visitors, amenity complexity and alternative measures on central location | Coefficient of variation
---|---
| (1) | (2) | (3) | (4) | (5) | (6)
Amenity complexity | 0.113∗∗∗ | 0.069∗∗∗ | 0.112∗∗∗ | 0.019 | 0.031∗∗ | 0.046∗∗∗
| (0.021) | (0.016) | (0.021) | (0.015) | (0.015) | (0.014)
Centrality of location |  | 0.116∗∗∗ |  |  |  |
|  | (0.011) |  |  |  |
Distance from center of mass |  |  |  $-$0.003 |  |  |
|  |  | (0.011) |  |  |
Distance from zero km stone |  |  |  |  $-$0.129∗∗∗ |  |
|  |  |  | (0.011) |  |
Distance from Deak ter |  |  |  |  |  $-$0.111∗∗∗ |
|  |  |  |  | (0.009) |
Distance from LISA center |  |  |  |  |  |  $-$0.104∗∗∗
|  |  |  |  |  | (0.012)
Nr POIs in category (log) |  $-$0.008 |  $-$0.006 |  $-$0.008 |  $-$0.004 |  $-$0.003 |  $-$0.006
| (0.008) | (0.007) | (0.008) | (0.006) | (0.007) | (0.007)
Nr visitors (log) | 0.087∗∗∗ | 0.069∗∗∗ | 0.086∗∗∗ | 0.052∗∗∗ | 0.046∗∗∗ | 0.054∗∗∗
| (0.010) | (0.008) | (0.010) | (0.006) | (0.007) | (0.008)
Constant | 0.216∗∗∗ | 0.172∗∗∗ | 0.219∗∗∗ | 0.381∗∗∗ | 0.361∗∗∗ | 0.347∗∗∗
| (0.034) | (0.030) | (0.035) | (0.032) | (0.031) | (0.030)
Observations | 2,742 | 2,742 | 2,742 | 2,742 | 2,742 | 2,742
R2 | 0.067 | 0.108 | 0.067 | 0.167 | 0.144 | 0.140
Adjusted R2 | 0.066 | 0.106 | 0.066 | 0.166 | 0.143 | 0.139
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

## S8 Dominant amenity categories of H3 hexagons

The second part of our empirical exercise (section 4.2 Diversity of visitors
to complex amenities) connects visitors to actual amenities. This is done by
mapping each point of interest (POI) from the Google Places API to a size 10
H3 hexagons ([46]). These hexagons are on average 15.000 $m^{2}$ area, which
is close to the buffer area of a point with a 70 meter radius. As we use the
amenity complexity values calculated for amenity categories (see Equation (6)
in the main text) to explain the diversity of visitors to size 10 H3 hexagons,
we need to assign a single amenity category to each hexagon with POIs. Figure
20 illustrates that most hexagons only have amenities in a single amenity
category, however, hexagons at dense, central locations often contain multiple
POIs from different categories.

Figure 20: Number of different amenity categories per size 10 H3 hexagons on
the map of Budapest (A) and on the map of the inner city (B). Distribution of
different amenity categories per hexagons (C). The colorbar applies for all
subplots.

We assign a dominant amenity category for each hexagon based on the local
frequency of POIs in amenity categories. Figure 21 visualizes our dominant
category selection process. $35.15$% of the hexagons have ambiguous amenity
category dominance and in these cases we simply choose the first category
listed. Table 11 illustrates in comparison to Table 2 of the main text that
our key findings are the same in case we focus only on amenities in H3
hexagons with a single amenity category or in case we only consider amenities
in H3 hexagons with an unambiguously dominant amenity category.

Figure 21: Illustration of the dominant amenity category selection. Different POIs over the hexagons (A) and the determined hexagon category (b). Table 11: Controlled correlations between the diversity of visitors and the complexity of amenities in case we only consider H3 hexagons with (1) a single amenity category or with (2) an unambiguously dominant amenity category | Coefficient of variation
---|---
| Single category | Dominant category
| (1) | (2)
Amenity complexity | 0.153∗∗ | 0.080∗∗∗
| (0.075) | (0.021)
Centrality of location | 0.061 | 0.127∗∗∗
| (0.059) | (0.012)
Nr POIs in category (log) |  $-$0.032 |  $-$0.010
| (0.024) | (0.008)
Nr visitors (log) | 0.144∗∗∗ | 0.063∗∗∗
| (0.052) | (0.008)
Constant | 0.154∗ | 0.181∗∗∗
| (0.080) | (0.034)
Observations | 151 | 1,849
R2 | 0.091 | 0.127
Adjusted R2 | 0.066 | 0.125
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

## S9 Alternative measures on the diversity of visitors to neighborhoods and
amenities

Table 12 supports the findings presented in Table 1 of the main text. It uses
the same model setting to illustrate the relationship between the diversity of
visitors to neighborhoods, neighborhood complexity and urban centrality, but
applies different measurements of the dependent variable. Besides the
coefficient of variation, the Gini index and the Theil index are used to
measure the diversity of visitors and all model version suggest similar
connections. Table 13 supplements the findings of Table 2 in the main text in
a similar fashion at the level of amenities.

Table 12: Controlled correlations between different measures on the diversity of visitors and neighborhood complexity | Coefficient of variation | Gini | Theil
---|---|---|---
| (1) | (2) | (3)
Neighborhood complexity | 0.125∗∗∗ | 0.088∗∗∗ | 0.056∗∗∗
| (0.036) | (0.018) | (0.012)
Centrality of location | 0.089∗∗∗ | 0.032∗∗ | 0.019∗
| (0.028) | (0.014) | (0.010)
Population (log) |  $-$0.050∗∗ |  $-$0.026∗∗ |  $-$0.016∗∗
| (0.022) | (0.011) | (0.007)
Nr visitors (log) | 0.039 | 0.018 | 0.011
| (0.029) | (0.014) | (0.010)
Nr POIs (log) | 0.006 |  $-$0.002 |  $-$0.002
| (0.023) | (0.011) | (0.008)
Constant | 0.363∗∗∗ | 0.198∗∗∗ | 0.068∗∗∗
| (0.057) | (0.029) | (0.019)
Observations | 186 | 186 | 186
R2 | 0.303 | 0.295 | 0.266
Adjusted R2 | 0.284 | 0.276 | 0.246
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 13: Controlled correlations between different measures on the diversity of visitors and the complexity of amenities | Coefficient of variation | Gini | Theil
---|---|---|---
| (1) | (2) | (3)
Amenity complexity | 0.069∗∗∗ | 0.035∗∗∗ | 0.023∗∗∗
| (0.016) | (0.007) | (0.005)
Centrality of location | 0.116∗∗∗ | 0.051∗∗∗ | 0.029∗∗∗
| (0.011) | (0.005) | (0.003)
Nr POIs in category (log) |  $-$0.006 |  $-$0.004 |  $-$0.002
| (0.007) | (0.003) | (0.002)
Nr visitors (log) | 0.069∗∗∗ | 0.032∗∗∗ | 0.016∗∗∗
| (0.008) | (0.004) | (0.002)
Constant | 0.172∗∗∗ | 0.100∗∗∗ | 0.017∗
| (0.030) | (0.014) | (0.009)
Observations | 2,742 | 2,742 | 2,742
R2 | 0.108 | 0.115 | 0.074
Adjusted R2 | 0.106 | 0.114 | 0.073
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

## S10 Diversity of non-local visitors to neighborhoods

Table 14 supports the findings presented in Table 1 of the main text, but the
models consider only the socio-economic diversity of non-local visitors. This
means that we excluded all third place visits to neighborhoods by devices with
identified home location inside the same neighborhood. Results are very
similar to our main models.

Table 14: Controlled correlations between the diversity of non-local visitors and the amenity complexity of neighborhoods | Coefficient of variation (non-local visitors only)
---|---
| (1) | (2) | (3) | (4) | (5)
Neighborhood complexity |  | 0.134∗∗∗ |  |  | 0.135∗∗∗
|  | (0.035) |  |  | (0.036)
Amenity diversity |  |  |  $-$0.169∗∗ |  |  $-$0.183∗∗
|  |  | (0.074) |  | (0.072)
Avg amenity ubiquity |  |  |  |  $-$0.046 |  $-$0.013
|  |  |  | (0.048) | (0.049)
Centrality of location | 0.113∗∗∗ | 0.070∗∗ | 0.113∗∗∗ | 0.107∗∗∗ | 0.067∗∗
| (0.026) | (0.028) | (0.026) | (0.027) | (0.028)
Population (log) |  $-$0.043∗ |  $-$0.040∗ |  $-$0.038∗ |  $-$0.038∗ |  $-$0.033
| (0.022) | (0.021) | (0.022) | (0.023) | (0.022)
Nr visitors (log) | 0.039 | 0.031 | 0.047 | 0.037 | 0.039
| (0.029) | (0.028) | (0.029) | (0.029) | (0.028)
Nr POIs (log) | 0.008 | 0.015 | 0.061∗ |  $-$0.004 | 0.070∗∗
| (0.023) | (0.022) | (0.033) | (0.026) | (0.033)
Constant | 0.403∗∗∗ | 0.337∗∗∗ | 0.330∗∗∗ | 0.436∗∗∗ | 0.267∗∗∗
| (0.055) | (0.056) | (0.063) | (0.065) | (0.073)
Observations | 186 | 186 | 186 | 186 | 186
R2 | 0.231 | 0.287 | 0.252 | 0.235 | 0.312
Adjusted R2 | 0.214 | 0.268 | 0.232 | 0.213 | 0.285
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

## S11 Amenity complexity and the diversity of visitors over 24 months

Figure 22 illustrates the relationship between diversity of visitors to
neighborhoods and neighborhood complexity over 24 months. The figure shows the
coefficients for neighborhood complexity from the regression setting presented
in Table 1 model (2) of the main text. It suggests that neighborhood
complexity does not have a significant relationship with the diversity of
visitors in 6 out of 24 months.

Figure 22: Regression coefficient of neighborhood complexity estimated for 24
months by model (2) of Table 1 in the main text. Different colors indicate
different levels of significance.

Figure 23 illustrates the relationship between diversity of visitors to
amenities and amenity complexity over 24 months. The figure represents the
coefficients for amenity complexity from the regression setting presented in
Table 2 model (2) of the main text. It shows that neighborhood complexity does
not have a significant relationship to the diversity of visitors in 8 out of
24 months. The differences between the two figures do not allow us to argue
for a strong impact of COVID-19 on visitation patterns.

Figure 23: Regression coefficient of amenity complexity estimated for 24
months by model (2) of Table 2 in the main text. Different colors indicate
different levels of significance.

## S12 Instrumental variable approaches to estimate the relationship
between neighborhood complexity and diversity of visitors

There are a number of potential unobserved factors that influence both
neighborhood complexity and the socio-economic diversity of visitors to
neighborhoods, creating a potential endogeneity problem when measuring their
relationship. To account for this potential endogeneity, we re-estimate our
results presented in Table 1 of the main text using different instrumental
variable (IV) approaches [2]. The IV estimation approach corrects for possible
endogeneity in regression settings by using variables (instruments) that do
not belong to the explanatory equation. The requirement for this is that IVs
are uncorrelated to the dependent variable (at least conditionally on the
level of the independent variable) but correlated with the main independent
variable (in our case, neighborhood complexity).

[10] argues that complexity measures constructed from the spatial distribution
of activities are potentially endogenous variables in many spatial research
settings. At the international level, [41] shows that economic complexity is
related to the distance of countries from economic centers, and as a result,
complexity indicators show spatial correlation. In the main text we present
that our measures of amenity complexity are also connected to the urban
centrality of locations. To account for this endogeneity issue we follow [43]
and introduce an IV which is constructed for each neighborhood by taking the
average neighborhood complexity of the three neighborhoods with the most
similar specialization pattern to the focal neighborhood. The logic behind
this IV is that neighborhoods with similar specialization patterns should also
have similar neighborhood complexity as the focal neighborhood, but the
complexity of the similar neighborhoods should not affect the visitation
pattern to the focal neighborhood and should not be connected to other
neighborhood specific unobserved characteristics. Table 15 presents the IV
regressions alongside the original OLS regression from the main text. The IV
estimation reinforces our original finding, however, the coefficient of
neighborhood complexity is less significant.

Table 15: Diversity of visitors to neighborhoods and neighborhood complexity: instrumental variable approach using similar specialization patterns | Coefficient of variation
---|---
| OLS | IV
| (1) | (2) | (3)
Neighborhood complexity | 0.125∗∗∗ |  | 0.074∗
| (0.036) |  | (0.044)
Neighborhood complexity (avg of 3 most similar) |  | 0.050∗ |
|  | (0.026) |
Centrality of location | 0.089∗∗∗ | 0.103∗∗∗ | 0.121∗∗∗
| (0.028) | (0.030) | (0.030)
Population (log) |  $-$0.050∗∗ |  $-$0.055∗∗ |  $-$0.045∗∗
| (0.022) | (0.022) | (0.022)
Nr visitors (log) | 0.039 | 0.050∗ | 0.036
| (0.029) | (0.029) | (0.029)
Nr POIs (log) | 0.006 | 0.002 | 0.002
| (0.023) | (0.023) | (0.023)
Constant | 0.363∗∗∗ | 0.409∗∗∗ | 0.375∗∗∗
| (0.057) | (0.056) | (0.059)
Observations | 186 | 186 | 186
R2 | 0.303 | 0.273 | 0.294
Adjusted R2 | 0.284 | 0.253 | 0.275
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

In another IV estimation setting, the historical separation of neighborhoods
from Budapest is used as an instrument for neighborhood complexity. The
current form of Budapest was only realized in 1950, when 59 municipalities
gave up their autonomy and were integrated into the capital. We create a dummy
variable for each neighborhood and use it as an IV which takes the value of 1
in case the neighborhood only became part of Budapest in 1950 and 0 otherwise.
The rationale behind using this variable as an instrument is that
municipalities that were independent before 1950 had an amenity structure
organized to serve the independent municipality (e.g. independent local
administration, marketplaces, libraries or post offices), while the already
integrated municipalities could rely more on the central facilities and
services of the capital. Consequently, historical separation of neighborhoods
could influence their complexity, but not the socio-economic diversity of
visitors to neighborhoods today (beyond its indirect effect through
complexity). Table 16 presents the IV regressions using historical separation
as an instrument alongside the original OLS regression from the main text. The
IV estimation reinforces our original findings, but the coefficient of
neighborhood complexity is less significant. Both of our instruments are
statistically valid.

Table 16: Diversity of visitors to neighborhoods and neighborhood complexity: instrumental variable approach using historical separation of neighborhoods | Coefficient of variation
---|---
| OLS | IV
| (1) | (2)
Neighborhood complexity | 0.125∗∗∗ | 0.485∗∗
| (0.036) | (0.209)
Centrality of location | 0.089∗∗∗ |  $-$0.004
| (0.028) | (0.072)
Population (log) |  $-$0.050∗∗ |  $-$0.031
| (0.022) | (0.028)
Nr visitors (log) | 0.039 | 0.007
| (0.029) | (0.038)
Nr POIs (log) | 0.006 | 0.024
| (0.023) | (0.030)
Constant | 0.363∗∗∗ | 0.167
| (0.057) | (0.125)
Observations | 186 | 186
R2 | 0.303 |  $-$0.079
Adjusted R2 | 0.284 |  $-$0.109
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01