# Street access, Informality and Development: A block level analysis across
all of sub-Saharan Africa

Luís M. A Bettencourt  University of Chicago, Department of Ecology and
Evolution, Chicago IL, 60637, USA  University of Chicago, Mansueto Institute
for Urban Innovation, Chicago IL, 60637, USA  Santa Fe Institute, Santa Fe NM,
87501, USA  corresponding author(s): Luís Bettencourt
(bettencourt@uchicago.edu), Nicholas Marchio<EMAIL_ADDRESS> Nicholas
Marchio  University of Chicago, Mansueto Institute for Urban Innovation,
Chicago IL, 60637, USA  corresponding author(s): Luís Bettencourt
(bettencourt@uchicago.edu), Nicholas Marchio<EMAIL_ADDRESS>
###### Abstract

Sustainable development is an imperative worldwide but metrics and data on
poverty and quality of life have remained too coarse and abstract to
characterize challenges adequately and guide practical progress. Nowhere is
this challenge greater than in Africa where we still know relatively little
about the systematic spatial details and scope of development. Here, we
leverage a complete, high-precision dataset of building footprints to identify
infrastructure deficits and infer informal settlements down to the street
level everywhere in sub-Saharan Africa. We identify a general pattern of
informality with urbanized areas showing, on average, greater access to
infrastructure and services than rural and periurban areas, each characterized
by a statistically consistent spectrum of uneven local development. We show
that our physical measures of informality are systematically associated with
many indicators of low human development, and that these form a single
principal component predicted by specific functional changes of the built
environment. These results demonstrate that the localization of sustainable
development is possible down to the street level at a continental scale and
provide a general distributed strategy for accelerating progress in
infrastructure and service expansion that taps local innovations in a way that
is equitable and context appropriate.

###### keywords:

Urbanization, Big Data, Complex Networks, Topology, Infrastructure, Informal
Settlements

The critical need for sustainable development has come into sharp focus
recently, along with the ambition to address associated challenges all over
the world in the decades ahead [1]. These imperatives have lead to landmark
international agreements to address climate change and achieve specific
sustainable development goals such as the worldwide eradication of extreme
poverty [2]. However, practical progress towards these goals, and the
integrated science and technology necessary to support them, has remained
slow. Two interlocking factors contribute to this situation. First, there is a
mismatch of scales between commitments made by national governments and
processes of human development, which take place primarily at smaller scales
in human settlements and their local communities [2, 3, 4, 5, 6]. Second, at
these smaller geographic scales and especially in lower income nations, there
is a lack of comparable, standardized, and sufficiently rich data [7, 2, 8, 9,
10], leading to calls for innovations towards their generation and analysis
[7, 4, 11].

Contrasting to these challenges, there has been significant recent progress in
our scientific understanding of cities and neighborhoods [12]. These
environments not only house a growing majority of the world’s population, but
also naturally promote systemic societal change [3, 12]. Specifically, the
process of urbanization is associated with long run improvements in many
interlocking facets of human development including higher real personal
incomes, greater access to healthcare and education, and expanded public
services [12, 3, 10]. This is because of both urban network (agglomeration)
effects in socioeconomic activities, which increase their productivity,
complexity and accelerate their results, and of economies of scale in
infrastructure and service delivery characteristic of the denser built
environment of cities [13, 14, 12]. Because of these general effects, it is
easier, faster and more productive to extend socioeconomic opportunities,
infrastructure, and services to populations in a larger city than it is to
create them in the first place in small towns and rural areas. As a result,
fast urbanization often induces increased rural to urban migration and results
in a general pattern of infrastructure and service delivery spreading along
the urban hierarchy, from larger cities to smaller settlements [3, 10]. This
dynamical pattern of development implies a sort of transition over space and
time, where signatures of higher human development are nucleated unevenly with
higher probability in better connected central locations in larger cities and
spread from there, eventually to all their constituent local communities and
other less urbanized regions. We will show below that this general pattern of
development is characteristic also of sub-Saharan Africa, and a feature of its
informal settlements [3, 15].

As a part of this uneven dynamics of development, fast urbanization often
becomes associated with the exacerbation of inequalities not only between
larger cities and rural areas but also on smaller scales, between
neighborhoods within each settlement [16, 3, 6]. The most critical of these
inequalities, because it entails many others, is the "challenge of slums" (or
informal settlements) [7, 15, 2, 17, 4]. These are neighborhoods resulting
from land settlement without coordinated urban infrastructure or legal
frameworks [18]. As a result, informal settlements are almost always initially
associated with multidimensional poverty, lack of basic services and insecure
land tenure [7, 2, 19]. In 2003, the United Nations declared slums "the face
of 21st century urbanization", motivating the first global studies and the
estimate of about 1 billion people living in informal settlements worldwide.
Central to addressing the problem was the enshrining of slum reduction and
eventual eradication (by 2030) in the United Nations Millennium (goal 1) and
Sustainable Development Goals (SDGs) target 11.1. Current assessments confirm
that we are late to meet this goal and estimate that 1.1 billion people now
live in informal settlements worldwide.

The present work started in support of data collections by local communities
in self-declared slums [20, 21, 2, 19]. In collaboration with federations of
non-governmental and local communities, it developed a set of standardized
surveys and detailed maps of buildings and public services in thousands
neighborhoods in 18 countries and 224 cities [21, 12]. As these and other
methodologies –including remote sensing [22, 23, 24, 25, 26], mobile phone
traces [27] and crowd sourced mapping [28]– continued to improve, an essential
spatial typology of informal settlements emerged defined by buildings without
street accesses. Lack of street access to informal places of residence and
work is the proximate common cause of many physical and socioeconomic
deficits, including the lack of official addresses and associated
socioeconomic stigma, unavailability of emergency services (such as fire
protection, ambulance) and disconnection from basic services, especially water
and sanitation which are piped along public ways [17, 29, 2, 19, 30]. Thanks
to extensive studies of informal settlements, we now understand that this
physical mismatch between buildings and street networks violates the basic
principles of urban built environments [17, 12]. This violation of urban
physical connectivity, entails a distinct cost-benefit relationship for slum
residents, trading off the possibility of settlement in the present against
lack of access to the network effects of cities. The result is an untenable
situation of latent but temporarily stunted human development. Because this
situation leads to high social costs and stresses not only for residents but
also for their societies, it must be resolved, typically by the extension of
urban infrastructure and services and the legal inclusion of such
neighborhoods into the physical and socioeconomic fabric of cities.

An additional difficulty deals with interpreting the function of urban built
environments in terms of spatial data on buildings and streets networks. Over
the last few years, topological methods capturing the detailed relational
nature of buildings to streets –regardless of specific geometry– have been
proposed, tested empirically and implemented computationally. These advances
now allow us, for the first time, to identify and characterize each street
block systematically over vast regions of the world [31, 17, 28, 12]. Here we
use the first complete dataset of building footprints for sub-Saharan Africa
to take this analysis of informality and development to a continental scale.
Our data consists of 5.4 million blocks, containing over 415 million buildings
in 89 nations and 1404 cities (Table S1), characterizing the living
environments of about 1.152 billion people across economically, culturally and
geographically diverse settings [15, 18]. Along with the analysis of street
access to buildings, we also characterize each block in terms of its number of
buildings, their sizes and spatial densities and estimate its resident
population by downscaling worldwide population raster maps to local street
block geometries [8]. This procedure creates a standardized, internationally
comparable dataset supporting the localization of sustainable development
metrics and population at the block level filling a substantial empirical gap,
especially in Africa [15, 18, 11]. We use this evidence to estimate informal
settlement populations locally across sub-Saharan Africa and to quantify
general patterns of human development connecting urban infrastructure networks
to social services and human capabilities, including measures of health,
education and income.

## Results

We now show how high-precision maps of buildings and streets can be analyzed
across scales to quantify the varying character of infrastructure deficits,
informal settlements and associated interlocking facets of socioeconomic
development. This analysis allows the simultaneous characterization of local
contextual factors down to the street level and the statistics of informality
across larger scales, from neighborhoods to cities, nations and the sub-
continent. Particularly important will be differences by levels of
urbanization, from urban cores to rural areas.

### Measuring infrastructure access across scales

The definition of an informal settlement (slum) developed by the United
Nations is "a settlement in which the majority of households experience one or
more of the following deprivations: lack of secure tenure, lack of access to
improved water sources, lack of improved sanitation facilities, insufficient
living space, poor structural durability of the dwelling". Except at the
extremes, these properties are difficult to measure both in terms of access to
the relevant information and because of inherent ambiguities leading to
difficulties of classification of a neighborhoods as slum versus a non-slum
[15, 32, 2]. A similar problem affects a growing number of studies attempting
a binary classification of neighborhoods using machine learning applied to
satellite and aerial imagery [33]. Some surveys evade these difficulties by
relying instead on community self-identification and assessing their
experience of existing services and living conditions [34, 20, 2, 30, 3].

Inspired by work co-producing mapping and socioeconomic data about informal
settlements with local organizations, we have created a simple but non-trivial
criterion for identifying informality, which can be measured objectively and
has deep roots in urban science: the lack of street access to buildings. This
quantity is at once of practical and fundamental interest because it speaks to
the processes by which cities assemble as self-consistent physical and social
networks [14, 12]. Water, electricity, drainage and sanitation are delivered
to each building via adjacent streets together with emergency services.
Addresses are also codified along municipal streets, regularizing many forms
of socioeconomic recognition and access including rights and obligations of
land tenure. For all these reasons, street access is not only a necessary
condition for development but also a strategic policy solution with many co-
benefits [29].

Empirically, the (lack of) physical connection to buildings is a local feature
of street networks, characterizing ’last mile’ access. Because it is a
relational quantity, it characterizes the spatial topology of cities
regardless of their structural geometry [17]. For example, it is independent
of whether street plans are curvy or form a grid, and of the scale of blocks
or buildings. These features make the identification of street access to
buildings a mathematical problem in topology [17, 12]. The relevant relation
is the (unobstructed) adjacency of buildings to street networks and to each
other, which can be captured via the construction of a block graph, Figures 1
and S1. The block graph is a network consisting of buildings (or land parcels)
as nodes and their adjacency as edges. Network analysis of these block graphs
identifies the access level of every building as the shortest path to any node
at the street boundary shown by different colors in Figures 1 and S1. This
approach is very efficient computationally because it decomposes the complex
(and seemingly intractable) geography of nations and cities down to many
independent blocks, which can be analyzed in parallel.

Recent work developed the mathematical and algorithmic methods to perform this
analysis in general block geometries [31, 17] but remained limited to small
scales by both data quality and computational efficiency. Here, we extend and
improve these methods and apply them to new (complete) datasets of building
footprints, street networks and population for the whole of sub-Sahararan
Africa, characterizing every block across the subcontinent, see Methods. Table
S1 provides summary statistics.

These methods quantify the severity of street access deficits to buildings in
terms of a single topological number with a simple intuitive meaning. The
block graph defines the summary statistic block complexity, $k$. This is the
distance from the most internal building in the block to the nearest street
access, measured as the minimum number of land parcels to be crossed. Block
complexity values of $k=1,2$ denote universally accessible (or "planned") city
blocks, where every building has direct street access or can do so via an
easement between buildings. Values in the range $k=3-4$ are less accessible
but can be the result of longer driveways, and the existence of non-
residential backyard buildings. Numbers progressively higher characterize
increasingly severe infrastructure deficits associated almost always with
informal settlements as supported by systematic visual inspection, see
Methods. Some false positives –blocks with large $k$ that are not informal
settlements– are sometimes found for particular types of institutional
campuses, such as colleges, hospitals, or airports but these are very rare and
easily identified by place names, building shapes and sizes.

Figure 1 illustrates the general analytical procedure. Using building
footprints and street network data along with population raster maps (at
larger scales, see Methods), we identify each city block as a geo-referenced
polygon delimited by streets and other natural or human-made boundaries. This
procedure is general and can be applied worldwide to produce uniquely
identifiable block-level spatial units similar to the systems used to collect
and report geographic census data in the U.S., or setores censitários in
Brazil. Figure 1A shows the decomposition of sub-Saharan Africa into nations
and human settlements (cities and towns), with the city of Lusaka (Zambia)
highlighted and expanded as an inset, Figure 1B. The square box is then
expanded in Figure 1C, to reveal its decomposition in terms of blocks with
colors revealing their $k$ complexity for a community area known as George. We
observe a number of blocks identified as informal settlements by high block
complexity (orange and yellow, left), as is also known from community surveys.
Other city blocks nearby are formal, in the sense that their buildings have
direct street access, and correspondingly low $k$. Figure 1D shows details of
informal and formal blocks, respectively. Informal settlement blocks are often
larger spatially than nearby accessible blocks, and show clear lack of street
access to internal buildings (black polygons). Table S1 and Figure S2 show
that, on average, buildings in blocks with greater complexity are smaller, and
that this is actually more prevalent in periurban and rural areas. Dead-end
streets are common in informal settlements (Figure 1D, E) as an incipient
means to create accesses to internal buildings at minimal cost [31, 17], a
process known as reblocking [31].

Figure 1: The block decomposition of sub-Saharan Africa. A. The decomposition
of the subcontinent into nations, cities and rural areas. B. Lusaka (Zambia),
the rectangular highlight is shown in Figure 1C, and a more detailed regions
showing all constituent blocks, in D. We observe a large variety block types
and shapes, delimited by streets shown in white. Building footprints are black
polygons visible in the panels of Figure 1E and F. For each block, a land
parcel is identified around each building (thin white lines): these parcels
form a graph expressing their spatial adjacency relationships, Figure S1.
Analysis of this block graph reveals how far each building is from the street
network, denoted in different colors. The block complexity $k$ is the number
of layers away from the street network for the most inaccessible building and
denotes the difficulty of extending infrastructure and services. The block in
Figure 1E is classified as informal by this measure, while the one in F is
formal. See https://www.millionneighborhoods.africa for an interactive map.

In addition to measuring each block’s complexity, we also produce block level
estimates of ambient (resident and working) population. To do this, we
projected population estimates from two different raster datasets in wide use
- LandScan [35] and WorldPop [36] \- down to the block level using building
footprint area, see Methods. In this way, we can characterize variations in
local population size and density as well as building area (table S1),
assessing crowding as estimated population per building area. The final
ingredient of our analysis deals with the aggregation of blocks into human
settlements and their characterization into settlement type categories: urban,
secondary urban, periurban and rural. The classification of a block as urban
denotes its inclusion in one city or town defined by the Global Human
Settlements Layer (GHSL). Because these boundaries are most often constructed
based on population density thresholds and spatial morphological features,
they are likely to underestimate actual urban expansion at low densities in
adjacent areas. To investigate this issue, we characterize blocks in the
peripheries of urban areas by creating a periurban land classification, which
comprises of a 10km buffer beyond the GHSL boundaries, corresponding to an
easily commutable region to the central city. Secondary urban areas are
smaller cities in the GHSL, which become associated to larger cities within
this buffer and together form candidate regions for larger conurbations
(Figures S4). Regions outside these three urban types, are classified as non-
urban, or rural.

### The statistics of informal settlements

Having characterized each block in each human settlement and rural region, we
can now create and characterize the statistics of infrastructure deficits and
inferred residential informality across scales. Figure 2 shows the frequency
distribution of population living in blocks with different $k$ complexity, by
settlement type and population size. The most salient feature of this
distribution is that it is very broad, Figure 2A. Figure 2B shows the
population decomposition in terms of type of settlement, indicating that by
our estimate, the majority of the population in sub-Saharan Africa (56%)
remains rural. Importantly, transitional periurban areas, likely accounting
for fast urban expansion, contain a total population around 200 million
people, comparable to urban cores [37]. Figure 2C shows the distribution of
population totals across different levels of spatial access showing that more
than half of the population of sub-Saharan Africa live in blocks with
substantial or extreme lack of infrastructure accesses, a number in the range
of 0.5-0.6 billion people. This is a new estimate for the total population
living in informal settlements across sub-Saharan Africa but note that the
majority is rural.

Besides producing calculations of aggregate population totals, the distinct
strength of these results lie in the localization of the challenge of
informality at the block level, and providing an objective spatial measure of
infrastructure deficits to estimate its severity. As such, our findings are
somewhat more positive than an estimate of the total number of people living
in informal settlements suggests. A fundamental takeaway from these results,
made possible by the extensive character of the analysis, is that they do not
support a simple dichotomy of neighborhoods classified as either slums versus
non-slums. Instead, we observe a broad spectrum of access deprivation, with
the most common neighborhoods in Figure 2A (median $k=3$) actually having
(almost) complete infrastructure access to each building. There is, however,
also a long tail of neighborhoods whose buildings are much less accessible,
including many extreme cases at $k>6$. Our results show that blocks with very
high $k$ are actually quite rare in central urban areas, see also Figure S3,
though there are clearly some well known cases. This finding has the important
consequence that many of the assumed characteristics of slums - being urban,
high population densities, and crowding- are not typical of the general
situation of informality in sub-Saharan Africa, which is much more rural and
also periurban and at low density, Figure S2. Surprisingly, crowding is much
more likely in rural areas where most buildings are very small (median area
20$m^{2}$, Figure S2), despite very low population densities at the larger
scales of blocks and regions, Table S1.

Figure 2: The distribution of population in blocks with different complexity
$k$, by urban levels across sub-Saharan Africa. A. Histogram of total
population in blocks with different $k$ and levels of urbanization. We see
that extreme infrastructure deficits are relatively rare in cities and occur
almost exclusively in urban peripheries and rural areas. B. The total
population of sub-Saharan Africa by urbanization type, showing that the
majority remains rural and periurban. C. Total population by levels of
infrastructure deficits $k$, showing that about 50% still live in blocks with
strong deficits.

Because blocks tile the entire territory, this type of analysis can be
produced at any relevant aggregate scale including individual cities, regions,
and nations. Figure 3 shows the spectrum of block complexity, $k$, for each of
the subcontinent’s largest urban areas, see also Figure S4 for conurbations.
The left panel shows urban areas sorted by population size with Lagos
(Nigeria) being the largest in the subcontinent with about 22.5 million
people. (Lagos is projected to grow to about 80 million by the end of the
century [38].) The right panel shows cities sorted instead by higher levels of
access deficits (higher $k$). We observe in general that larger African cities
actually outperform their rural areas in infrastructure access, see also
Figure S3-S4, but none has completely addressed the challenge of slums. Some
cities such as Antananarivo (Madagascar) remain mostly informal, while others
such as Dakar (Senegal), Cape Town or Johannesburg (South Africa) have
provisioned more extensive street access, though many clearly identifiable
spatial pockets remain (see interactive map, Methods). The challenge is more
severe for conurbations, because these enlarged city definitions include
periurban areas where lower density informal settlements are common, Figure
S4. Aggregating these trends at the national level (Figure S5) confirms that
the least accessible blocks and the majority of population experiencing access
deprivation is rural, but also identifies nations with substantially less
access, such as Chad, Madagascar, Mozambique, Somalia, Sudan, and South Sudan.

Figure 3: Population spectrum of informality for the major cities of sub-
Saharan Africa. A. Cities ranked by population showing, for example, that
Lagos (Nigeria) likely already provides infrastructure access to $>65$ % of
its population ($k\leq 3$). B. Cities ranked by higher levels of
infrastructure deficits, $k$. Antananarivo (Madagascar) stands out as the
subcontinents most informal city, but cities such as Dar Es Salaam (Tanzania)
or Kampala (Uganda) also present significant challenges. Cities with the
highest levels of access provision include Dakar (Senegal), Mogadishu
(Somalia) and the cities of South Africa, but none in the continent has yet
completely addressed the challenge of slums.

### Linkages between street access and human development

We now demonstrate that the block complexity $k$ has a deeper functional
meaning, not only expressing spatial access deprivation but also entailing
many other dimensions of low human development [15, 2]. This includes direct
physical issues, such as lack of water and sanitation, but also a broad set of
socioeconomic characteristics such as lower education, wealth and worse
health.

At present there are no standard local data collections for human development
indicators across sub-Saharan Africa [15, 11]. Partially filling this gap,
there is a long tradition of demographic and health surveys (DHS) supported by
international agencies in collaboration with national statistics, see Methods.
These surveys are less extensive than our block metrics, and moreover lack
spatial precision. To compare the two types of evidence, we aggregated block
data to subnational administrative subdivisions made available in the DHS
survey data. The spatial scale of Figure 1B gives a sense that this
aggregation mixes together heterogeneous neighborhoods with significantly
different characters [3], but we demonstrate below that correlations using
these averages remain universally consistent and significant.

Figure 4: The association between street access to buildings and different
dimensions human development. Measures of service provision, education and
wealth are mutually correlated in demographic and health surveys and well
characterized by the first component in a principal component analysis of 67
distinct variables, see Table S2-S3. Panels A-D show the variation of this
component with block complexity $k$ at the regional level, across nations and
urban areas. In all cases the relationship is negative showing that higher $k$
block complexity (and inferred informality) is systematically associated with
lower female literacy, lower wealth and lower access to basic services, see
also Figure S6

Using these spatially aggregated data, we performed a number of statistical
analyses to establish the link between a large set of socioeconomic
development measures and spatial access deprivation measured by block
complexity, see Tables S2-S3 and Figures 4 and S6. First, we correlated the
variation of 67 different dimensions of human development on changes in block
complexity, $k$, Table S2. We grouped these metrics in thematic groups
including direct estimates of economic well-being, education and literacy,
health, basic services, and household characteristics, including quality of
housing and crowding. All these variables show systematic and significant
correlations on block complexity across the subcontinent. For example, urban
slum populations estimated at the national level are strongly correlated with
higher average block complexity. Child mortality, underweight and stunting
increase with larger $k$, while the fraction of live births in health
facilities decreases. Higher block complexity is negatively correlated with
measures of education at all levels (primary, secondary and higher) and median
years of education. Higher spatial access deprivation is also associated with
lower female literacy, see Fig. 4A, though there are some notable exceptions
such as Namibia, well known for its successful National Literacy Program,
showing the potential for policy. Measures of access across all basic
services, as expected, show a consistent pattern of increasing deficits with
larger $k$, as do decreasing quality of housing measured by earth/sand and
’natural’ floors. Measurements of crowding and wealth support this general
picture associating multidimensional deprivations to block complexity, but the
pattern of correlations adds interesting detail. For example, the fraction of
households with 1-2 persons per sleeping room (no crowding) decreases with
larger $k$, while larger numbers increase, as does the average number of
persons per sleeping room. Parallel to these findings, the fraction of
households in the two highest wealth quintiles decreases with $k$, while it
increases in the lower 3 quintiles, especially the lowest. We also find that
greater wealth inequality, measured by regional Gini coefficients, is
associated with larger spatial access deprivation. Measures of economic well-
being by consumption follow a similar pattern, with households with a
refrigerator, private car, computer, television or mobile phone decreasing
with $k$, the latter importantly showing a weaker negative correlation.

All these statistical relationships are stable across nations and to the
inclusion of control variables. In fact, these relationships become
statistically much stronger (higher $R^{2}$) when treated at the national
level via country fixed effects, and stronger still when we control for
settlement type, via the share of population living in urban areas, Table S2.

Because we observe that these diverse measures of human development are
mutually correlated, in agreement with studies in other local contexts [3, 10,
6], we also characterized their joint variation with $k$. To do this, we
performed a principal component analysis across regions and identified the
leading collective dimensions of variation. The first principal component
explains most of the variation ( $\sim 48$%), Table S3. Figure S4 illustrates
this behavior showing the variation of four different socioeconomic variables,
specifically female literacy, access to water, sanitation and household
wealth, see also Figure S6. These results also show that denser (and
explicitly more urban) regions perform better on average in all dimensions of
human development relative to less dense and more rural regions. Table S2-S3
quantifies how country fixed effects and the share of urban population
significantly improves these correlations, but that other factors such as
building size, building to land area ratio, and population density matter
relatively little once block complexity and urban levels are factored in.

We conclude that there is a clear and systematic pattern of multidimensional
development across scales, with greater local street access and urbanization
(at the regional level) facilitating socioeconomic opportunity, education,
better health, and improved access to all basic services. The relatively
larger multidimensional deprivations in rural and periurban areas speak to the
necessity, as well as the opportunity, to extend existing physical and
socioeconomic access to these territories [18, 37].

## Discussion

We have shown that high-precision spatial data, specifically the combination
of georeferenced building footprints and street networks, can be used to
quantify physical access deficits, which in turn underlie an array of
conditions associated with human development from basic services to heath and
socioeconomic opportunity. We have shown that blocks with severe lack of
street access to buildings, measured by the $k$ topological index, can be
identified as informal settlements leading to a new objective method for
producing localized street level estimates of population living in poverty,
the main target of sustainable development goals 1.1 and 10.1 [2].

Where they have been mapped, this physical measure of lack of street access to
buildings coincides with self-declared slums, and with multidimensional
indicators of disadvantage measured by the best available international
demographic and health surveys. While the present analysis deals with sub-
Saharan Africa, we have created open-source tools that allow the
generalization of these results to any other context where complete building
footprints and street networks are available. It will be especially important
in future work to extend the current analysis to other world regions,
especially to Asia and South America where fast urbanization remains markedly
informal but where comprehensive detailed characterizations are still lacking.
It will also be critical to assess improvements in infrastructure delivery
over time, to track localized sustainable development goals along with other
local metrics of human development at the level of neighborhood communities.

There are a few qualifications and caveats to the present results that we
expect will be resolved as data and methodologies continue to improve. At
present, building footprints are identified from manual tracing and remote
sensing imagery using a combination of edge detecting algorithms, machine
learning, and quality controls by human operators. This process achieves very
good results, easy to verify against high precision images. Nevertheless, any
analysis of this type fails to identify important information including
building types, height, materials, and services all of which speak to issues
of quality of life and human development [2, 31]. Crowd-sourced data is also
becoming excellent and may help fill these gaps but, at present, still remains
incomplete and shows some inconsistencies especially at the smallest scales.
Above all, these methods must become better integrated with the living
experience of places known to local communities, civic organizations and local
governments [20, 2, 19]. The convergence of these methods and perspectives is
already gathering speed and scope towards producing richer, localized physical
and socioeconomic data. Thus, we expect the kind of localized, systematic
analysis introduced here to continue to improve and become standard in the
very near future, providing a systematic framework for tracking and
understanding deficits, inequalities, and successes in infrastructure and
service delivery, development and urban evolution at the community scale
everywhere on Earth.

The systematic inference of informal settlements developed here points to a
number of general features of urban development, which provide novel
ingredients to innovation and policy. First, there is no basis for a
classification of local communities as a dichotomy of "slums versus no slums",
as has been assumed in both policy discussions and supervised classification
methods from remote sensing imagery [19, 25, 33]. Instead, our analysis points
to the existence of a continuous spectrum of access deprivation, with most
neighborhoods in sub-Saharan Africa experiencing a range of deficits of
infrastructure and services, and only a relatively much smaller set being very
deprived, denser and more complex, consistent with the findings of case
studies [30]. Moreover, neighborhoods in the larger cities of sub-Saharan
Africa tend to show fewer and less severe deficits of access infrastructure
than in their corresponding rural and periurban areas, where, on the other
hand, the nature of poverty and informality is very different [30, 19]. In
this sense, the infrastructure deficits across sub-Saharan Africa present a
number of diverse challenges that include relatively small but systemic
improvements in most neighborhoods in urban areas, intense interventions in
rarer but denser urban slums [34], and comprehensive infrastructure
development in relatively easier but extensive periurban and rural areas. The
block level maps introduced here transform these vast challenges into a much
more treatable modular problem, where each block can be considered separately
and whereby context appropriate solutions can be co-produced between resident
communities and local governments. Other co-benefits, such as the generation
of cadastral maps and addresses are naturally created by this process (Figure
1C,D, S1) and can support context-appropriate institutions promoting secure
land tenure, land use rights and responsibilities, and a formalized tax base
for local governments [18].

Despite a number of recent claims based on macroscopic indicators that African
cities are lagging in terms of economic development, and that African
urbanization is fundamentally different because of the abundance of informal
settlements [39, 40, 15, 41, 42], we would argue –without trivializing
absolute levels of deprivation– that the current evidence points in a
different direction. We find that African cities, with variation as in Figure
3, are doing significant better on average than their adjacent periurban and
rural areas across every dimensions of development, including infrastructure
delivery, basic services, healthcare access, and socioeconomic development
[15]. Moreover, this gradient of development along the urban hierarchy, from
larger to smaller cities and towns, is typical of past patterns of
urbanization processes elsewhere [32, 12, 3, 10].

Along with these practical considerations, the empirical evidence introduced
here supports an emerging general understanding of the connection between
urbanization and human development. Urban science has increasingly focused on
the role of street networks supporting mobility and socioeconomic
interactions, from which they derive socioeconomic value and predictable
quantitative properties related to the population size of cities [14, 12, 29].
It is precisely the dividend of these connections that is only latent in fast
developing cities with generalized infrastructure deficits. As physical access
networks become more present in the near future, they are thus predicted to
also expand and diversify socioeconomic networks and render cities more
innovative and productive [12]. Connected to this feedback between
infrastructure and socioeconomic networks is an increasingly clear view of
human development as the expansion of physical and socioeconomic connectivity.
Thus, low human development is a personal condition of disconnection,
associated with more local social networks dedicated primarily with coping and
survival in the absence of supportive platforms, such as meaningful access to
basic services, health care, public safety, and social institutions. This view
of development as a partly physical network process, clearly more present in
higher income cities, provides concrete strategies for human-centric policies
that create virtuous cycles of change, whereby investments in (missing)
physical connectivity can more than pay for themselves by generating broad
socioeconomic development, which in turn can support stronger institutions,
infrastructure and services [15].

The prospect of a general localized approach to sustainable development means
that millions of neighborhoods around the world will be developing in parallel
over the next decades, connecting to their local infrastructure networks and
becoming increasingly formalized in the sense of public services, addresses
and land uses, adding to their resilience to climate change and other stresses
[19]. This shared global experience brings online a vast peer to peer network
of local innovators solving similar challenges, and supporting the creation of
general knowledge and new technologies truer to the living experience of
cities. In this way, we may leverage the growth of our scientific
understanding of cities of all sizes and the growing possibilities of larger
data to support and accelerate human development that is faster, more
universal, and more sustainable.

## Methods

Datasets: Building footprints data were produced by Ecopia Landbase Africa in
2022, powered by Maxar imagery and accessed via DigitizeAfrica Platform at
https://platform.ecopiatech.com. Street network data were obtained from
OpenStreetMap available at www.openstreetmap.org, retrieved from the Geofabrik
at https://download.geofabrik.de/africa.html. Population data were obtained
from 2 worldwide raster maps by LandScan [35], available at
https://landscan.ornl.gov, and WorldPop [36], available at
https://data.worldpop.org/GIS/Population/Global_2000_2020_Constrained. Urban
area geometries were based on the Global Human Settlements Layer (GHSL) Urban
Centre Database [43] at https://ghsl.jrc.ec.europa.eu. Periurban areas are
defined as a 10km spatial buffer around GHSL boundaries. National slum
population estimates were obtained from the United Nations Human Settlement
Programme (UN-Habitat) Global Urban Indicators Database 2020, available at
https://data.unhabitat.org/pages/housing-slums-and-informal-settlements.
Demographic and health survey data are available at https://api.dhsprogram.com
and https://spatialdata.dhsprogram.com.

Block generation and population estimates: Block delineation is based on all
connected streets in OpenStreetMap, from which we excluded the category of
"footpaths" as these are reported irregularly and are not typically associated
with infrastructure access. Blocks are defined as land geometries (polygons)
circumscribed by street, roads and other boundaries such as rivers and
coastlines. The code to create block geometries is available at
https://github.com/mansueto-institute/geopull. Block level population
estimates are produced by down-allocating population from spatial grids at
larger scales (1km and 100m for LandScan and WorldPop, respectively) to each
block proportionally to building area.
Validation, analysis and visualization: We inspected and validated building
footprints against satellite imagery in a variety of locations to confirm
(almost) full completeness and accuracy, except for very small buildings,
which are likely not residential. We created an interactive visualization of
the data and analysis that can also be used for local assessment at
www.millionneighborhoods.africa, showing data for each block in terms of its
$k$ complexity, estimated population, building counts and building and land
areas. This also includes a population density map at high (block) precision,
along with urban type classifications. Correlation analysis between these
block characteristics and demographic and health indicators were obtained at
subnational administrative units compatible with DHS surveys. Principal
component analysis was performed over 67 indicators (dimensions) in 219
subnational region-year observations, as specified in Tables S2 and S3. The
DHS data used in the analysis of correlations covers 238 administrative
regions across 22 countries and 40 unique surveys taking place between 2010
and 2021, producing 367 unique survey observations.
Data and software: The database is available online at
www.millionneighborhoods.africa/download. Code for the analysis in this paper
is available at https://github.com/mansueto-institute/kblock-analysis. Code
for generating the underlying database is available at
https://github.com/mansueto-institute/kblock.

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## Acknowledgements

We thank Io Blair-Freese and the Bill and Melinda Gates Foundation for access
to the Ecopia building footprints data. We thank Anni Beukes, Genie Birch,
Christa Brelsford, and Pedro Conceição for discussions and audiences at the
UN-Habitat Assembly and Slum Dwellers International for useful comments. Dylan
Halpern, Manuel Martinez, Merritt Smith, Idalina Sachango, Cooper Nederhood,
and Satej Soman at the University of Chicago contributed to the underlying
methods, code, and visualizations.

## Author contributions statement

LB, NM conceived the paper; NM performed data analysis and visualizations; LB,
NM wrote the paper. All authors reviewed the manuscript.

## Supplementary Materials

### Supplementary Tables

Urban | Buildings | Population | Blocks | Building | Building | Building- | Population | Block
---|---|---|---|---|---|---|---|---
level | number | (LandScan) | number | area $m^{2}$ | density $ha^{-1}$ | block area ratio | per building | complexity
Urban | 60,863,684 | 265,447,669 | 1,506,939 | 97.12 | 16.67 | 0.16 | 4.36 | 3.70
Secondary Urban | 11,414,255 | 45,242,376 | 242,781 | 106.78 | 13.04 | 0.139 | 3.96 | 3.68
Periurban | 71,107,900 | 197,082,233 | 1,045,786 | 63.65 | 0.58 | 0.0037 | 2.77 | 9.42
Rural | 271,633,601 | 645,214,883 | 2,604,990 | 40.81 | 0.11 | 0.0004 | 2.38 | 9.65
Total | 414,019,440 | 1,152,987,161 | 5,400,496 | 54.8 | 0.16 | 0.0009 | 2.78 | 8.01
Table S1:  Summary Statistics of buildings, population and block statistics by urban level. Note the changes in density from more to less urbanized areas and the opposite trend in service access expressed by rising block complexity. Note also the relative population weight and incipient infrastructure access in periurban areas. Group |  Subgroup |  Variable |  Spearman- rank Correlation |  N |  Used in PCA |  PC1 loading |  PC2 loading
---|---|---|---|---|---|---|---
Economic well-being |  Livelihoods | % of men employed in agriculture | 0.6312 | 265 | Yes | -0.151 | -0.07
% of men employed in skilled manual labor | -0.3649 | 265 | Yes | 0.103 | -0.068
% of men employed in unskilled manual labor | -0.4669 | 245 |  |  |
% of men employed in prof., technical, mgmt. | -0.3811 | 265 | Yes | 0.088 | -0.003
% of women employed in agriculture | 0.4495 | 266 | Yes | -0.123 | -0.108
% of women employed in domestic labor | -0.4353 | 180 |  |  |
% of women employed in unskilled manual labor | -0.4308 | 246 |  |  |
% of women employed in prof., technical, mgmt. | -0.4632 | 266 | Yes | 0.118 | -0.074
Wealth | % in the lowest wealth quintile | 0.4229 | 367 | Yes | -0.089 | -0.082
% in the second wealth quintile | 0.3702 | 367 | Yes | -0.086 | -0.157
% in the middle wealth quintile | 0.2655 | 367 | Yes | -0.037 | -0.119
% in the fourth wealth quintile | -0.221 | 367 | Yes | 0.072 | 0.077
% in the highest wealth quintile | -0.4888 | 367 | Yes | 0.105 | 0.168
Wealth index Gini coefficient | 0.2956 | 363 | Yes | -0.112 | -0.091
Household property | % of households possessing a computer | -0.6058 | 190 |  |  |
% of households possessing a refrigerator | -0.6721 | 367 | Yes | 0.156 | 0.062
% of households possessing a mobile telephone | -0.4358 | 367 | Yes | 0.12 | 0.092
% of households possessing a television | -0.7078 | 367 | Yes | 0.158 | 0.088
% of households possessing a private car | -0.6475 | 367 | Yes | 0.149 | 0.055
Education & literacy |  Education | Median years of education (both sexes) | -0.5471 | 272 | Yes | 0.158 | -0.104
Median years of education (males) | -0.5573 | 272 | Yes | 0.153 | -0.097
Median years of education (females) | -0.5496 | 272 | Yes | 0.158 | -0.11
% of age 6+ with no education | 0.5329 | 272 | Yes | -0.138 | 0.16
% of age 6+ who attended secondary school | -0.6123 | 272 | Yes | 0.157 | -0.114
% of age 6+ who attended higher education | -0.6693 | 272 | Yes | 0.14 | 0.033
Net primary school attendance rate | -0.5337 | 228 |  |  |
Net secondary school attendance rate | -0.644 | 228 |  |  |
Women's education & literacy | Gross parity index for gross secondary school | -0.4939 | 228 |  |  |
% of women who are literate | -0.5743 | 367 | Yes | 0.148 | -0.135
% of young women who are literate | -0.5641 | 367 | Yes | 0.145 | -0.145
% of young women who cannot read at all | 0.5631 | 367 | Yes | -0.145 | 0.146
Net primary school female attendance rate | -0.5415 | 228 |  |  |
Net secondary school female attendance rate | -0.6931 | 228 |  |  |
% of women with secondary or higher education | -0.6283 | 367 | Yes | 0.161 | -0.128
% of females age 6+ with no education | 0.54 | 272 | Yes | -0.142 | 0.153
% of females age 6+ who attended secondary school | -0.6421 | 272 | Yes | 0.163 | -0.103
% of females age 6+ who attended higher education | -0.6444 | 272 | Yes | 0.143 | 0.004
% of women w/weekly access to newspaper, TV, radio | -0.4913 | 297 | Yes | 0.125 | -0.011
% of women with no access to mass media | 0.6695 | 297 | Yes | -0.141 | 0.006
% of women who have a bank account | -0.6586 | 96 |  |  |
% of women who own a mobile phone | -0.5492 | 114 |  |  |
Group |  Subgroup |  Variable |  Spearman- rank Correlation |  N |  Used in PCA |  PC1 |  PC2
---|---|---|---|---|---|---|---
Health |  Women | % of women who are thin with $<$ 18.5 BMI | 0.4615 | 240 |  |  |
% of married women met need for family planning | -0.5551 | 266 | Yes | 0.121 | -0.156
% of live births delivered at a health facility | -0.5844 | 272 | Yes | 0.118 | -0.053
Children | Child mortality rate | 0.4899 | 265 | Yes | -0.125 | -0.033
Infant mortality rate | 0.378 | 266 | Yes | -0.096 | -0.08
Postneonatal mortality rate | 0.4428 | 266 | Yes | -0.098 | -0.113
Under-five mortality rate | 0.4614 | 265 | Yes | -0.121 | -0.061
% of 1 year olds who received all 8 basic vaccinations | -0.3309 | 271 | Yes | 0.039 | -0.093
% of children age 6-23 months fed 5+ food groups | -0.4641 | 266 | Yes | 0.112 | 0.025
% of children stunted ($<$-2 SD of height for age) | 0.5784 | 254 | Yes | -0.123 | -0.06
% of children underweight ($<$-2 SD of weight for age) | 0.6631 | 254 | Yes | -0.13 | 0.092
% of children wasted ($<$-2 SD of weight for height) | 0.4655 | 254 | Yes | -0.098 | 0.117
% of children under age 5 classified as having anemia | 0.4255 | 334 | Yes | -0.103 | 0.138
Water, sanitation & hygiene |  Sanitation & hygiene | % of population with sanitation facility in dwelling | -0.447 | 127 |  |  |
% of population with basic sanitation service | -0.5484 | 367 | Yes | 0.125 | 0.061
% of population with an improved sanitation facility | -0.602 | 367 | Yes | 0.137 | 0.081
% of population using open defecation | 0.6534 | 367 | Yes | -0.098 | 0.006
% of population with soap & water for handwashing | -0.4487 | 236 |  |  |
% of population with soap available for handwashing | -0.3566 | 236 |  |  |
Water | % of population with basic water service | -0.6031 | 367 | Yes | 0.134 | 0.1
% of population using improved water | -0.4811 | 367 | Yes | 0.122 | 0.107
% of population with improved water on premises | -0.6278 | 367 | Yes | 0.143 | 0.18
% of population with limited water service | 0.3798 | 367 | Yes | -0.062 | -0.006
% of population using an unimproved water source | 0.4818 | 367 | Yes | -0.122 | -0.106
% of population using water piped into dwelling | -0.4843 | 367 | Yes | 0.126 | 0.12
% of population with water under 30 min. round trip | 0.3133 | 367 | Yes | -0.113 | -0.205
% of population with water over 30 min. round trip | 0.4946 | 367 | Yes | -0.093 | -0.051
% of population with water on the premises | -0.5966 | 367 | Yes | 0.139 | 0.187
Household Characteristics |  Crowding | Mean persons per sleeping room | 0.4202 | 367 | Yes | -0.079 | 0.292
% of households with 3 generations | -0.0503 | 367 | Yes | -0.018 | -0.015
% of households with 1-2 persons per sleeping room | -0.3612 | 367 | Yes | 0.069 | -0.293
% of households with 3-4 persons per sleeping room | 0.4115 | 367 | Yes | -0.091 | 0.246
% of households with 5-6 persons per sleeping room | 0.2102 | 367 | Yes | -0.042 | 0.273
% of households with 7 + persons per sleeping room | 0.1907 | 367 | Yes | -0.028 | 0.257
Utilities | % of population cooking in the house | -0.2343 | 266 | Yes | 0.113 | -0.043
% of population using clean fuel for cooking | -0.442 | 358 | Yes | 0.133 | 0.064
% of population using solid fuel for cooking | 0.4575 | 367 | Yes | -0.137 | -0.058
% of population with electricity | -0.6992 | 367 | Yes | 0.153 | 0.087
% of population with no electricity | 0.699 | 367 | Yes | -0.153 | -0.087
Floors | % of population with earth/sand floors | 0.5702 | 367 | Yes | -0.128 | -0.068
% of population with natural floors | 0.6058 | 367 | Yes | -0.134 | -0.056
Slums | % of country’s urban population living in slum | 0.6243 | 42 |  |  |
households, reported by UN-Habitat |  |  |  |  |
Table S2:  Demographic and health surveys (DHS) subregional correlational and factor analyses on $k$ and other spatial variables. | Univariate | Country effects |  Country effects & controls
---|---|---|---
Adjusted R2 | 0.2146 |  | 0.6098 |  | 0.8179 |
Covariate predictors of PC1 | Coefficient | P-value | Coefficient | P-value | Coefficient | P-value
Intercept | 4.7073 | 0.0000 | 0.8503 | 0.5036 | -4.4860 | 0.0003
Block complexity | -0.6590 | 0.0000 | -0.6228 | 0.0000 | -0.2996 | 0.0000
Population share in urban areas |  |  |  |  | 10.6840 | 0.0000
Share of buildings under $31m^{2}$ |  |  |  |  | 8.4182 | 0.5882
Building footprint to block area ratio |  |  |  |  | -36.1866 | 0.0449
Population per hectare |  |  |  |  | 0.0635 | 0.0550
Cameroon |  |  | 4.4184 | 0.0007 | 4.2147 | 0.0000
Guinea |  |  | -0.1785 | 0.8953 | -0.0409 | 0.9652
Niger |  |  | -2.0468 | 0.2033 | -2.0022 | 0.0709
Côte d’Ivoire |  |  | 0.8060 | 0.5870 | 1.2584 | 0.2196
Gabon |  |  | 7.0766 | 0.0000 | 9.1024 | 0.0000
Namibia |  |  | 11.4452 | 0.0000 | 12.4638 | 0.0000
Sierra leone |  |  | -0.1818 | 0.9117 | 0.9420 | 0.4137
Togo |  |  | 1.3337 | 0.4548 | 1.5926 | 0.1946
DR Congo |  |  | 0.9241 | 0.5316 | 0.7654 | 0.4529
Ghana |  |  | 5.6949 | 0.0002 | 5.7902 | 0.0000
Lesotho |  |  | 4.1297 | 0.0084 | 6.9151 | 0.0000
Angola |  |  | 3.7609 | 0.0041 | 2.6877 | 0.0032
South Africa |  |  | 12.5949 | 0.0000 | 13.0673 | 0.0000
Benin |  |  | 1.6002 | 0.2727 | 1.5403 | 0.1282
Mali |  |  | 0.4987 | 0.7578 | 0.8045 | 0.4742
Nigeria |  |  | 4.9953 | 0.0055 | 4.3431 | 0.0005
The Gambia |  |  | 3.0856 | 0.0697 | 4.6341 | 0.0003
Liberia |  |  | 1.6457 | 0.3811 | 2.8718 | 0.0296
Mauritania |  |  | 6.7953 | 0.0000 | 6.6507 | 0.0000
Principal Component 1 (PC1) is the dependent variable and is taken from the
PCA on 67 DHS indicators. PC1
explains 47.6% of the variance in the PCA, followed by PC2 at 8.6%.
Regressions were based on 219 observations
at the subnational administrative level. The Spearman-rank correlation between
block complexity and PC1 is -0.709.
The model is a ordinary least squares regression.
Table S3: Principal component analysis of selected DHS variables versus block
complexity $k$. Note that the adjusted R2 increases with country fixed effects
and controls for other spatial variables. Of these only the region’s level of
urbanization (population share in urban areas) is significant.

### Supplementary Figures

Figure S1: Block graph for Figure 1E. To create a block graph and calculate
the block’s $k$ complexity, we create a land parcel decomposition of the land
area of the block, with each parcel encompassing a building (and its
footprint), see methods. A the block graph is then created by connecting the
center of each parcel to all spatially adjacent parcels. Parcels adjacent to
streets are marked as external. Each parcel (building) is then characterized
by its shortest distance to one of these external nodes in terms of number of
links in the block graph, corresponding to parcels to be crossed. The block’s
$k$ complexity is longest such distance, corresponding to the shortest
distance to the street network from the blocks least accessible parcel. As a
matter of procedure, we create a parcel map in each block and a
characterization of the distance to the street network of each building, shown
in color gradient. The color characterizing each block in Figure 1C, and in
the interactive visualization map at https://millionneighborhoods.africa is
that corresponding to this least accessible building.  Figure S2: The
distribution of building footprint area, across sub-Saharan Africa by urban
type. A. Histogram of building numbers by area and urban type. B. The relative
distribution of building sizes by urban type. Note that rural areas are
generally characterized by smaller buildings, with the median peaking around
20$m^{2}$. There is a much greater variety of building sizes across urban
areas (principal and secondary) especially in the range 20-200$m^{2}$, where
buildings are generally larger, see Table S1. Periurban areas have an
intermediate character between urban cores and rural areas. Figure S3: The
relationship between average block complexity and population size, by
settlement type, urban to rural in nations of sub-Saharan Africa. Note how
lack of street access to buildings is predominantly a feature of rural areas,
whereas urban areas in most nations have lower $k$, see also Table S1.
Periurban areas show much larger variability, with good access in several
nations (South Africa, Zimbabwe, Botswana), but manifestly low in many others
(Sudan, South Sudan, Chad, Mozambique). These results suggest varying degrees
of planning and infrastructure development across African nations, and also
broader regions. Figure S4: The spectrum of informality across major sub-
Saharan African conurbations. This figure is analogous to Figure 3, but uses
conurbations as its functional urban unit, instead of GHSL definitions.
Conurbations group together GHSL cities with their 10km periurban buffer
regions, and result naturally in larger urban areas.  Figure S5: Summary of
distribution of block complexity across nation in sub-Saharan Africa. The left
panel shows results nationwide, while the left panel is limited to
conurbations, see also Figure S3. We see significantly smaller block
complexity in urban areas in general, and some nations with substantially less
access than others, such as Madagascar, Mozambique, Somalia, Sudan, South
Sudan and Chad. Figure S6: The extended version of Figure 4, showing the
correlation of a larger number of diverse indicators along their main
principal component versus $k$ block complexity. Symbol size denotes
population density (denoting urban regions for larger symbols) and colors show
the specific indicator variation along the PC1 variation with block
complexity, $k$. We observe that measures of advantage (female literacy,
access to services) are systematically anti-correlated with block complexity,
while measures of disadvantage (poor housing quality, lower wealth) are
correlated.