11institutetext: Complex Systems Group, Aalto University, Finland
22institutetext: Semantic Computing Research Group (SeCo), Aalto University,
Finland
https://seco.cs.aalto.fi 33institutetext: HELDIG – Helsinki Centre for Digital
Humanities, University of Helsinki, Finland
https://heldig.fi
44institutetext: Huygens Institute for the History of the Netherlands:
Amsterdam, NL

# Communication Now and Then: Analyzing the Republic of Letters as a
Communication Network

Javier Ureña-Carrion 11 0000-0003-2763-9747 Petri Leskinen 22
0000-0003-2327-6942 Jouni Tuominen 2233 0000-0003-4789-5676 Charles van den
Heuvel 44 0000-0001-9638-400X Eero Hyvönen 2233 0000-0003-1695-5840 Mikko
Kivelä 11 0000-0003-2049-1954

###### Abstract

Huge advances in understanding patterns of human communication, and the
underlying social networks where it takes place, have been made recently using
massive automatically recorded data sets from digital communication, such as
emails and phone calls. However, it is not clear to what extent these results
on human behaviour are artefacts of contemporary communication technology and
culture and if the fundamental patterns in communication have changed over
history. This paper presents an analysis of historical epistolary metadata
with the aim of comparing the underlying historical communication patterns
with those of contemporary communication. Our work uses a new epistolary
dataset containing metadata on over $150\,000$ letters sent between the 16th
and 19th centuries. The analyses indicate striking resemblances between
contemporary and epistolary communication network patterns, including dyadic
interactions and ego-level behaviour. Despite these positive findings, certain
aspects of the letter datasets are insufficient to corroborate other
similarities or differences for these communication networks.

##  1 Introduction

New communication technologies and their digital traces have revolutionized
the social sciences by providing new tools for understanding human behaviour
[1, 2], and permitting to model society as a network of diverse and
multifaceted relationships [3, 4, 5, 6, 7]. This has resulted in important
insights regarding patterns of human communication [8, 9] and the structure of
social networks [10, 3]. However, these analyses have been mainly described
with data from contemporary human societies such as mobile phone calls, emails
and online platforms. Although these phenomena have been observed in a myriad
of contemporary communication media, the extent to which these phenomena are a
product of current technologies and practices, or whether they are also
present in other historical contexts and thus a characteristic of human
behaviour is unclear as this question has mostly been analysed from
theoretical perspectives [11, 12]. In this paper, we study a large historical
epistolary dataset under a behavioural framework, and investigate whether
letters —a major communication channel during the previous centuries— reflect
patterns of human behaviour known to be present in contemporary communication.

Much of the progress in understanding the communication patterns and social
behaviour has been made by conceptualising them as patterns in networks —a way
of modelling social systems where individuals (or nodes) interact with each
other (via links or edges) [13]—. Communication metadata has provided crucial
access for understating social networks as it allows us to construct exchange
networks as proxies for the underlying social system that generated them.
Figure 1 depicts an example of how interactions can be represented as
networks: from a history of communication between two people or nodes, we
create links or edges if there has been an interaction, and analyze both
reconstructed networks and the time series of interactions.

Figure 1: Network reconstruction from recorded interactions. (i), In a simple
social system, individuals A-D contact each other through directed letters,
emails, phone calls, etc; (ii), we model undirected interactions as a time
series of contact events, reconstructed from recorded contact metadata
(sender, receiver, timestamp). Datasets are constrained to observation periods
or snapshots (blue and red). (iii) Given an observation period, we can
reconstruct a static network by creating links between nodes A-D if we observe
at least one contact (solid lines). We do not account for a link if we do not
observe data during the observation period (dashed lines). A common technique
is to assign a link weight $w$ (numbers) based on the number of contacts.

This approach has confirmed several prominent sociological theories. Milgram’s
notion of “six degrees of separation” [14], where any two people are expected
to be at a path of at most six people away from each other, was popularised in
the 60s but only later studied with large-scale data, and is now known as
small-world phenomena [15]. Similarly, in the 70s, Mark Granovetter
hypothesised the "strength of weak ties", which states that the rarely-used
weak social links keep networks connected by bridging separate social groups.
This was later shown to hold at the level of a country using a communication
network of millions of mobile phone users [3, 16].

These new approaches have also produced completely new theories of social
behaviour and the system-level phenomena that emerges from it. One of the
first key findings was large degree heterogeneity. That is, the number of
neighbors varies considerably, where a majority of people have little
connections yet a small number of individuals are highly connected. This has
major implications on, e.g., disease and information spreading [17]. The
number of connections is of course limited as there are temporal, spatial and
cognitive constraints into maintaining connections, which has lead to common
strategies that people follow in managing their communication in the
contemporary settings [18, 19, 9]. In this sense, people have robust social
signatures: they tend to devote a similar amount of attention to their active
circles of contacts, even if the circle of contacts changes [18, 19].

Large-scale data has also facilitated the analysis of different dimensions of
temporality in human behaviour, including sequential events [20, 21] and daily
or regular cycles [22]. Event sequences are often not regular or uniformly
random, but the contacts are organised in bursts [20, 21]. This tells us about
the possible processes of how the communication originates from the
individuals, such as internal models of priority queues. Despite the small-
world phenomena, information does not circulate as freely as burstiness can
hinder information flow [21, 20, 15].

The idea that communication mediums have an effect on societal structures and
practices has been actively studied from historiographical perspectives.
Harold Innis in ”The Bias of Communication” [11] explored the notion that each
historical epoch is distinguished by dominant forms of media consonant with
the institutional power. Inspired by him, Marshall McLuhan stressed the impact
of electronic technology on human behaviour and social organization [12].
Social theories that have informed social network analysis have also been used
in historical contexts. Lux and Cook [23] used the concept of weak ties in
scientific exchange in the seventeenth century by contrasting the role of
closed circles of academies in England and France and open networks of
interactions that facilitated, e.g., the work of Dutch scientists. The small-
world phenomena has also been studied on historical networks [24] in the ”Six
Degrees of Francis Bacon” project [25].

While letters are not automatically collected into large databases similar to
some forms of digital communication, recently there have been large and
concentrated efforts to collect and unify such large historical epistolary
data sets distributed across different countries and collections. Metadata
about the letters have been aggregated and provided for the research community
through web services, such as Europeana111http://www.europeana.eu,
Kalliope222http://kalliope.staatsbibliothek-berlin.de, The Catalogus
Epistularum Neerlandicarum333http://picarta.pica.nl/DB=3.23/, Electronic
Enlightenment444http://www.e-enlightenment.com,
ePistolarium555http://ckcc.huygens.knaw.nl/epistolarium/, the Mapping the
Republic of Letters project666http://republicofletters.stanford.edu,
SKILLNET777https://skillnet.nl, correspSearch888https://correspsearch.net and
the Early Modern Letters Online (EMLO)
catalogue999http://emlo.bodleian.ox.ac.uk [26, 27, 28, 29].

We contextualize epistolary communication by examining the Republic of Letters
(RofL). The RofL was a self-proclaimed community of scholars between the
fifteenth and eighteenth centuries that consisted of overlapping networks. In
these networks scholars communicated by letters and exchanged knowledge, news,
and material objects such as books [27]. This group is often described in
idealistic terms as a self-regulating open community of scholars not limited
by political borders or religious convictions. Nevertheless, these scholars
could face persecution on account of religion and politics and often had to
choose their words carefully due to the risk that their letters were
intercepted, duplicated and even published [30]. Openness, confidentiality and
secrecy co-existed and had an impact on the topological nature and development
of these networks of scholars in which knowledge exchange was not merely
reciprocal, but hierarchical as well [26, 31]. These overlapping networks were
in continuous flux. New members were often introduced by central gatekeepers
who played a strong regulating and mediating role to keep these networks in
balance, but that could also fall apart, resulting in structural holes [32].

Some characteristics of epistolary communication might be analogous to
contemporary forms of communication. The RofL was a community organized around
specific social foci that included scholars and the clergy [33]. In current
settings, such focused communication occurs in emails sent within
organizations or in specialized internet forums. A major difference between
epistolary and contemporary channels is related to immediacy. In epistolary
communication, the time between contacts had a considerable time gap
constrained by exogenous factors such as distance and logistics, which
contrasts with digital channels where waiting times depend mostly on users’
behaviour [12]. Now, both historical and contemporary datasets have biases. In
the former case, a major source of bias stems from the data-collection process
itself [34, 35], with researchers slowly building an epistolary archive from
different sources; in the latter, auto-recorded data is usually one of many
communication channels and temporal windows are shorter.

Our goal is to investigate how several of the prominent results on
contemporary communication hold for letters sent between 1510–1900. We analyse
correspSearch, a large-scale epistolary data set representative of the RofL
and compare it to four reference data sets on contemporary communication using
email, two digital platforms, and mobile phones (see Materials and Methods).
We find striking resemblance between historical and contemporary communication
patterns, including in the distribution of dyadic temporal features, the
robustness of social signatures, and certain network-wide characteristics. We
note, however, that there are also considerable structural differences. For
these negative results, we can’t assure whether they are caused by social
phenomena or the biases from the collection process of historical data.

##  2 Results

We compare metadata from correspSearch with four modern communication
datasets. Each of these datasets consists of logs of interactions including a
sender, a receiver and a timestamp. We highlight the diversity of
communication channels, which include mobile phone calls (Mobile), emails
(Email), Internet community boards (Forum) and wall-posting on a social
platform (Platform) (see Materials and Methods). Taken together, these
datasets correspond to several instances and channels of auto-recorded
communication, and we claim that these epistolary datasets represent a
historical equivalent of contemporary human communication.

We present findings of common similarities and differences between the
historical and contemporary datasets from four analytical approaches: (i)
aggregate static networks, (ii) features of pairwise communication (iii)
relationship between communication and local topology, and (iv) social
signatures of ego networks.

###  2.1 Analysis of the static graph

We first model communication as aggregate static networks [36], where the
temporal dimension is projected out by disregarding the contact times. This
approach allows us to determine whether there are any major structural
similarities between the historical and contemporary networks. As several of
the static network features have been studied in historical correspondence
datasets [34, 35, 37], we describe these results only briefly, and include a
more detailed analysis on Supplementary Information 1. We find that the
epistolary network snapshots are similar to other communication networks only
to some extent, with the main difference stemming from over-represented nodes.

The interpretation of static networks differs over large observation periods.
For our correspondence data, dyads are constrained to participant’s active
life, but the overall network can be thought of as the overlapping activity
from dyads, where larger structures might not represent, e.g., communities,
but temporally overlapped communities, which are more difficult to interpret.
We ameliorate some of these issues by aggregating data over different 50-year
periods, resulting in a series of static graphs.

We present a selection of common network statistics: centrality measures, tie
overlap and the distribution of shortest paths. Centrality measures are
informative of the relative importance and roles of a node in the network. In
this sense, degree $k$ measures the number of connections, while betweenness
$C_{B}$ is related to the number of shortest paths that pass through a node.
Tie overlap $O$ is link-level statistic used to assess whether an edge is
contained within overlapping circles of friends, or serves as a "bridge", and
the distribution of shortest paths $l$ helps characterize the small-world
phenomena.

On Figure 2 we compare static network statistics for the correspondence and
reference datasets. We find similarities in terms of the heavy-tailed degree
distribution [38], decaying centrality measures and average shortest-path
distribution, with epistolary networks exhibiting small-world phenomena even
at 50-year aggregation periods. Nevertheless, in correspondence networks some
nodes have an outsized impact as compared to most important nodes of the
reference networks. This is reflected in (i) slower decay for the degree
distribution, where the tail reflects an upwards flattening curve in the log-
log axis; (ii) overall larger centrality measures, e.g., some nodes score
$C_{B}>0.5$ betweenness, meaning that more than half of all shortest paths go
through them as opposed to all other networks having $C_{B}<0.08$. Notably,
the overlap distribution might the most affected from sampling, as it requires
sampling dyads as opposed to nodes. Th mobile phone network, the data set with
most individuals, displays the most differences when compared to the other
references, with fast degree and betweenness centrality decay, and longer
shortest paths.

Figure 2: Static features of communication networks, where the top (bottom)
rows contains features of the correspondence (reference) networks. Epistolary
datasets are aggregated in 50 year periods. Columns represent distributions of
(left to right) degree $k$, betweenness centrality $C_{B}$, topological
overlap $O$ and average shortest path length $l$. For ease of comparison, we
do not include individual data points, but present averaged binned values.

###  2.2 Features of human communication

We now explore how communication occurs between pairs of individuals, where
the focus is on different tie-level temporal dynamics, and not only on the
network structure. Figure 3 (i) depicts a visual example of approaches to
modelling communication sequences, where we obtain statistics from a time
series of interactions, such temporal stability $TS$, the inter-event times
$\tau$ and burstiness $B$. The total contact count $w$ has been used in
communication networks as a proxy for tie strength. Theoretically, Granovetter
[39] characterized four dimensions of tie strength: time, emotional intensity,
intimacy and reciprocity. In practical terms, however, these dimensions are
not straightforward to observe from interaction data, whether because of
incompleteness or because of lack of a natural metric or measure [40]. In the
Granovetter sense, however, the proxies for tie strength inform of topological
roles of ties, where weaker ties serve as bridges between overlapping circles
of friends [39, 41].

Figure 3: Temporal features of human communication. (i) Visual representation
of different temporal features for similar number of contacts, $w$. (i, a)
Temporal stability $TS$, where we only consider the first and last times
during the observation period. (i, b) Estimation of the inter-event time (IET)
distribution $\tau$, the elapsed time between consecutive events.(i, c)
Example of bursty behaviour, where bursts of consecutive calls are followed by
longer IETs. The burstiness coefficient is defined as
$B=\frac{\sigma-\mu}{\sigma+\mu}$ for $\mu$, $\sigma$ the mean and standard
deviation of $\tau$. (ii) Empirical distribution of number of contacts $w$ for
the epistolary dataset and four reference datasets. (iii) Empirical
distribution of temporal stability $TS$ for the epistolary and reference
datasets. For each case, we plot the distributions conditioned on link weight
quartiles. For ease of comparison, we do not include individual data points,
but present averaged binned values.

Figures 3 (ii-iii) shows statistics of the number of contacts $w$ and temporal
stability $TS$, respectively. Aggregate contacts $w$ are highly inhomogeneos
for all datasets, displaying heavy-tailed decay. Note that $w$ directly
impacts many temporal features. For this reason, we show distributions
conditioned on the number of contacts $w$ categorized by quartiles. On the
other hand, $TS$ displays major inter- and intra-dataset variability. Chiefly,
we identify a mix of quartile-independent sharp decay (CorrespSearch, Email),
heavy-tailed decay (Platform, Forum) or quartile-dependent growth and decay
(CorrespSearch, Email, Forum and Mobile). These different patterns might arise
due to an interplay of the observation period and tie decay. In Mobile we do
not expect to observe tie decay since the observation window is short [7, 42],
and thus the $TS$ differs conditioned on $w$ quartiles. Email and Letters, on
the other hand, display a mixture of the latter behaviour and sharp decay,
constrained by people’s active life (within a company, in the case of Email).

The distribution of times between consecutive contacts an individual makes,
known as inter-event times (IETs), is an important feature of human
communication that has undergone extensive scrutiny in the contemporary
communication patterns [43, 15, 21, 44, 45]. In epistolary data, IETs have
been analysed for only a handful of exceptionally prominent individuals, and
these finding indicate similarities between contemporary and correspondence
data [46, 47]. We expand on this work by focusing on large-scale behaviour and
in other statistics. Just as with the degree distribution, we find that IETs
tend to be very heavy-tailed and bursty [43, 15]. This means that the time
between events shows high variability, with long resting times followed by
short bursts of consecutive contacts.

On Figure 4 we focus on two statistics of the IET distribution — mean $\mu$
and burstiness $B$—. We uncouple $\mu$ from the number of contacts by scaling
the distribution by $\mu_{w_{i}}$, the mean distribution value for the
quartile category $i$. Previous research has shown that the distributions of
$\mu/\mu_{w_{i}}$ collapse onto a single distribution for all different
$w_{i}$ [43, 15, 36]. We replicate this result for most of our reference
datasets and for Letters, suggesting that the IET distribution for epistolary
data follows a pattern observed before for multiple large contemporary
communication data sets [43, 15, 4], and for the set of prominent individuals
in historical correspondence [46, 47]. We would expect people in close contact
to have short average IETs [41]; nevertheless, given the large timespan of the
epistolary data, the closeness of contacts could change throughout a person’s
lifetime.

All datasets display larger burstiness values for larger $w$, with the
epistolary data following similar average values the Platform and Email
datasets ($B$ around -0.19, 0.02, 0.14 for the first three quartiles of
Letters, Platform and Email; the last quartiles are 0.28 for Letters, 0.34 for
Platform and 0.20 for Email). Although burstiness has been explained by
behavioural patterns, such as mentally prioritising tasks [20] or cyclic
activity periods [45], some of the bursty character of epistolary data could
also be explained by the fact that news sharing and copying played an
important role in scholarly correspondences [48, 49].

Figure 4: Distribution of different values derived from the IET distribution
for correspSearch and our four reference datasets. The scale is days for
correspSearch, and seconds for the rest of the datasets. (i) Scaled mean IET
$\mu/\mu_{w}$, (ii) Burstiness coefficient $B$.

###  2.3 Granovetter Effect

We now examine the Granovetter effect, the theory states that strong links are
characterized by overlapping circles of friends, whereas weak links serve as
bridges [39]. This phenomena has been empirically observed by measuring the
strength of ties via contact calls, although it can also be observed for
several communication features by uncoupling from $w$ [41]. In empirical
social network analysis, the embeddedness of a tie can be measured via
topological overlap [3, 41].

We explore the Granovetter effect on Figure 5 by comparing overlap with $w$,
$TS$ and $\mu$. We find an association between some of the features and
overlap, with a visible effect for all datasets using $w$. This indicates that
correspondence data exhibits a salient feature of social networks, where user
behaviour tends to be found within local community structures. Notably, for
$TS$ we did not find a clear association for the epistolary data, as well as
for $\mu$ in the period 1775-1825. This might be related to sampling biases in
the network and in the time-series. In the first case, overlap is a measure
based on triads, which tend to be less likely to be sampled. Second, tie-level
dynamics might be affected by irregular sampling at different time periods.
This could explain why we observe the effect for $\mu$ in 1525-1575 but not in
1775-1825.

Figure 5: Granovetter effect for different features of communication on (left
to right) two snapshots of correspSeach (1525-1575) and reference datasets
Platform, Email and Forum (the effect has already been descibed in Mobile by
[41]). The embeddedness of ties, as measured by topological overlap, changes
in association with behavioural communication features, although not always in
a linear fashion. Shaded area represents 80% of the distribution. Features of
communication: (i) number of contacts $w$, (ii) temporal stability $TS$ and
(iii) Mean IET $\mu$. The Granovetter effect is most visible for $w$. Using
$TS$ as a proxy for tie strength we do not observe the effect for
correspSearch and we only observe it partly for Platform. For $\mu$, the
effect (decrease of overlap with larger average IET) is visible for the period
1525-1575 and partially for larger values of Forum.

###  2.4 Social Signatures

Ego networks, where the focus is on central nodes (egos) and their immediate
neighbors (alters) serve as useful characterizations of user behaviour. We
focus on social signatures, the idea that people divide their attention to
their high-ranking contacts in a persistent fashion across time and uniquely
to each ego [18, 19]. This does not mean that the alters don’t change — they
are highly dynamic—, but the attention devoted to high-ranking alters is
persistent. We inspect the ego networks of different people at consecutive
snapshots, where on each snapshot we create an ego network with the number of
outgoing contacts as link weights, where we focus only on outgoing contacts to
characterize the behaviour of the ego. Afterwards, we build the social
signature by ranking the alters and obtaining the fraction of outgoing
contacts.

In the seminal work where social signatures were observed for the first time
[18], Saramäki et al. divided the observation period into three snapshots,
thus obtaining three social signatures for each individual. They compared
social signatures for different intervals using the Jensen-Shannon Divergence
(Signature Distance $d$), a measure for comparing probability distributions,
and for reference they also compared social signatures to other individuals.
To adapt their analysis to our dataset, we incorporate two filters regarding
the number of alters during an interval, and the length of the interval. We
determine social signatures on a interval of size $b$, measured in years for
Letters, Email and Forum, and in months for Platform and Mobile. Following
[18], we compare social signatures for a given individual in $m=3$ adjacent
time intervals, and we compare signatures of other individuals during time
intervals of the same length. We determine a limit on the minimum number of
out-neighbors $n_{o-ng}$ that an ego must have during all intervals in order
to be a valid social signature, and we vary this parameter for a range of
values.

Figure 6 depicts the results for our analysis of social signatures for filter
values $n_{o-ng}=5$, and different bin sizes $b$ depending on the dataset; we
were, however, able to replicate the results of [18, 19] for all datasets and
for all filter values in Letters (see Supplementary Material 2). This suggests
that individualized patterns of communication that are consistent are not a
feature of contemporary communication networks, but were also persistent in
older and less immediate forms of communication as well. Even more, our
results hold for observation windows ranging from 1 to 10 years, and totaling
comparisons ranging 3 to 30 years considering three observation windows. This
indicates that these individual patterns can be observed not only in shorter
timescales, but also in periods spanning a large proportion of an adult life.

Figure 6: Comparison between self-distances $d_{self}$ and reference distances
$d_{ref}$ for ego networks of all datasets. The average self distances are
smaller than average reference distances for all parameter combinations,
implying that social signatures tend to be more similar for the same person
during different times, than to other people’s signatures. We performed a two-
sided T-test for difference in means, finding that for all datasets the mean
$d_{self}$ differed from $d_{ref}$ with all estimated p-vales $<10^{-13}$. The
estimated means for all datasets are: Letters $\hat{d}_{self}=0.218\pm 0.048$
and $\hat{d}_{ref}=0.302\pm 0.008$; Platform $\hat{d}_{self}=0.241\pm 0.025$
and $\hat{d}_{ref}=0.292\pm 0.002$; Email $\hat{d}_{self}=0.191\pm 0.019$ and
$\hat{d}_{ref}=0.317\pm 0.0001$; Forum $\hat{d}_{self}=0.189\pm 0.019$ and
$\hat{d}_{ref}=0.235\pm 0.001$; Mobile $\hat{d}_{self}=0.162\pm 0.014$ and
$\hat{d}_{ref}=0.227\pm 0.002$. Confidence intervals for the mean reported at
95%.

##  3 Discussion

We used common methods for analyzing social networks and applied them to a
large epistolary dataset in an attempt to uncover whether major differences
exist between contemporary and historical communication networks. For
reference, we used four contemporary datasets of communication data. Our
results strongly suggest that prominent characteristics of contemporary
communication networks are also found in historical contexts, validating that
these characteristics are related to fundamental human behavior, not only to
specific communication mediums practices. Despite these major positive
results, we also found differences in the contemporary and historical
communication patterns. We might attribute these negative results to
differences in the completeness of the datasets, since we depend on letters
that have survived and been included in collections. We note, however, that
they might also stem from differences in the use of media and communication
practices.

We divided our analyses in four main parts: global network structure and
characteristics, dyadic communication patterns, their relationship to local
topology, and analysis of ego networks. Regarding global structures, we found
the epistolary datasets to be both highly-local and deeply connected—in the
sense that most nodes have a very small number of connections, while still
maintaining relatively short average shortest path distributions. However, we
also found that a majority of nodes are under-represented in the network,
having less-than-expected connections. Indeed, since epistolary datasets tend
to focus on relevant historical figures, we centre the rest of our analysis on
dyadic interactions and ego networks.

Dyadic interactions display major similarities both in terms of the number of
contacts and in the distribution of inter-event times, even when considering
that the latter follows naturally different scales. Our results suggest that
major features of dyadic communication can be described with known mechanisms
of average IET decay, and that the overall burstiness distribution is in line
with contemporary communication channels. This is slightly striking, as one
could expect that limitations in using letters, such as less immediacy, could
imply greater regularity in communication. Further analyses, however, could
reveal how burstiness varies across several years.

We also found some evidence that epistolary networks also reflect the
Granovetter effect, where stronger ties are contained within overlapping
circles of friends, while weaker serve as bridges. To some extent, our most
interesting results were related to ego networks, possibly due to more control
in filtering come complete samples of ego networks. In this case, we found
that individuals in previous centuries communicated in a similar manner than
we do today: uniquely to individuals and persistent in time.

####  3.0.1 Acknowledgements

We thank Dirk van Miert, and Sebastiaan Derks for discussions and an the
possiblity of using ePistolarium data in our research. Thanks to Sebastian
Dumont for providing the correspSearch data and discussions. Our work is
continuation of the collaborations in the EU COST action Reassembling the
Republic of Letters and with University of Oxford in the Cultures of Knowledge
project and the Early Modern Letters Online service. Funding for the current
work was provided by the Academy of Finland and the EU project In/Tangible
European Heritage (InTaVia)101010https://intavia.eu.

##  4 Materials and Methods

###  4.1 Data

We include four datasets of contemporary human communication that encompass
different communication channels and environments, including email data,
mobile calls and online postings. More specifically:

Table 1: Datasets analyzed and compared in this paper Dataset |  Content |  Observation Period |  Source
---|---|---|---
Platform |  Wall-posting on Facebook in New Orleans, where a directed link is created if a user posts on another user’s wall. Data obtained from crawling public profiles in January 2009, each link tracks activity for one year after the first communication event. Total of $\sim 41$K nodes, $\sim 183.5$K edges and $\sim 854.6$K wall posts. |  1 year |  [50]
Email |  Dataset of emails between employees of Enron Corporation, obtained as part of an investigation into the Corporation’s collapse. Sampling might focus on 150 users. Total of $\sim 20$K users, $297.5$K edges and $\sim 1.1$M emails. |  1998-2004 |  [51]
Forum |  Activity on a movie forum, where a contact is created if a user comments on a thread posted by another user. Total of $\sim 6$K users, $\sim 138.1$K edges and $\sim 1.4$M thread comments. |  7 years |  [52]
Mobile |  Call Detail Records of mobile phone calls from an operator in a European country in 2007, where the operator had approximately 20% market share. We used a reduced version of the full dataset, where we focused on a region of the country. The small version of the dataset has $\sim 174$K nodes, $\sim 190$K edges and $\sim 6.8$M phone calls. |  4 months |  [3]

The Letters datasets comes from the aggregated data service correspSearch [53]
provided by the Berlin Brandenburg Academy of Sciences and Humanities. This
dataset includes metadata about ca. 135,000 letters sent in 1510–1900.

All data we used had been anonymized from source for all reference datasets,
and for the purpose of our research, we also used an anonymized version of
Letters. These datasets provide fruitful insights into modern human
communication. Mobile and Platform contains data a large user database,
allowing us to examine communication patterns at regional scales in both
European and North American contexts. The sampling of both datasets is foci-
independent in the sense that it does not follow specific societal units
within their region. Platform, however, it still represents a sample of people
with public Facebook profiles. On the other hand, Email and Forum contains
information from specific contexts (a company and an online community), and
thus their interactions might follow certain structures. In the case of Email,
we might expect that the sampling methodology that favors certain users. The
Letters dataset constitutes a unique example of human communication
encompassing five centuries of communication data across different countries
and time periods. This presents both unique opportunities and challenges, as
some of the common assumptions and techniques used for communication networks
might not hold true. Notably, these datasets include letters from high-ranking
personalities of religion, politics and science from several European
countries, and constitutes a (non-random) sample from a communication network
spanning five centuries.

The epistolary datasets have been transformed into Linked Data and published
on the Linked Data Finland platform111111https://ldf.fi [54] according to the
Linked Data publishing principles and other best practices of W3C [55],
including, e.g., content negotiation and provision of a SPARQL endpoint.
However, the data are at the moment not publicly available on the Web due to
copyright issues under negotiation with the owners of the primary metadata.

###  4.2 Static Network Construction

We construct static networks from communication data following the commonly-
used process described by [36] and [3]. We process data in the form of logs,
which in its most basic form include information of a sender, a receiver and a
timestamp. This holds both for the epistolary datasets and the modern
reference data. We create an undirected edge between nodes if we have observed
at least one letter between, but we keep track of the time series of
interactions for further analysis.

###  4.3 Temporal features

We derive different statistics based on the distribution of IETs. For a
sequence of interaction times of at least length three,
$\\{t_{0},t_{1},\ldots,t_{n}\\}$, we obtain the $k$th inter-event time
$\tau_{k}=t_{k+1}-t_{k}$, and estimate moments from this distribution from the
empirical observations $\\{\tau_{k}\\}$. We use the Kaplan-Meier estimator
[56], which considers censored data, as a means to correct for lack of data in
epistolary contexts. We thus obtain $\mu(\tau)$ (in the text $\mu$) and
$\tau_{\sigma}$ , the mean and standard deviation of our IETs. We use the
burstiness coefficient as proposed by [43], which is defined as
$B=(\tau_{\sigma}-\tau)/(\tau_{\sigma}+\tau)$. We measure temporal stability
in terms of the first and last observed interactions, $TS=t_{n}-t_{0}$.

For most temporal features, we plot distributions conditioned on quartiles of
$w$. Given the heterogeneity of $w$ it is not straightforward to partition
data into bins of equal size. In Table 2 we show the composition of quartiles
for each dataset. Notably, only Mobile is partitioned into bins of roughly
equal sizes (as percentage), for all other datasets, $q_{1}$ is
disproportionately large.

| $q_{1}$ | $q_{2}$ | $q_{3}$ | $q_{4}$
---|---|---|---|---
Dataset | $\%w<=2$ | Contacts | Percentage | Contacts | Percentage | Contacts | Percentage | Contacts | Percentage
CorrespSearch | 0.709 | 3-4 | 0.477 | 5-7 | 0.162 | 8-16 | 0.17 | >16 | 0.19
Platform | 0.578 | 3 | 0.425 | 4-5 | 0.208 | 6-9 | 0.169 | >9 | 0.20
Email | 0.734 | 3 | 0.434 | 4-5 | 0.182 | 6-10 | 0.185 | >10 | 0.198
Forum | 0.649 | 3 | 0.358 | 4-5 | 0.154 | 6-14 | 0.243 | >14 | 0.245
Mobile | 0.146 | 3-5 | 0.28 | 6-13 | 0.235 | 14-39 | 0.237 | >40 | 0.248
Table 2: Quartile composition for each dataset. The first numerical column
contains the fraction of linksn that have either one or two contacts, and
which were thus not used to compute temporal features. The latter columns
contain the composition of each quartile, including their ranges of contacts
and the percentage of links in that category.

###  4.4 Granovetter effect

For the Granovetter effect, we measure the overlapping circles of friends
between an edges via topological overlap. For $i,j$ two nodes, and
$\mathcal{N}(i)$ the set of neighbors of node $i$, the topological overlap is
the Jaccard similarity between the sets of neighbors

$O_{ij}=\frac{|\mathcal{N}(i)\cap\mathcal{N}(j)|}{|\mathcal{N}(i)\cup\mathcal{N}(j)|}$
(1)

##  5 List of Abbreviations

  * •

RofL: Republic of Letters

  * •

EMLO: Early Modern Letters Online

  * •

IET: Inter-event Time

### Authorship

J.U.C., M.K. and E.H. conceived the main ideas. J.U.C. and M.K. designed the
analysis, and J.U.C. performed the analysis. P.L., J.T. and J.U.C collected
the data and contributed with analytic tools. C.V.D.H. contextualized
historical data and designed analysis. J.U.C. took the lead in writing the
manuscript, to which all authors contributed.

### Data Availability

All datasets except Mobile are available online. Mobile is not publicly
available due to a signed non-disclosure agreement, as it contains sensitive
information of the subscribers. The epistolary dataset is being integrated in
the LetterSampo system[57, 58], underway for publishing and using epistolary
linked data on the Semantic Web, a new member in the Sampo series of Linked
Open Data services and semantic
portals121212https://seco.cs.aalto.fi/applications/sampo/ [59].

### Code Availability

A selection of the networks analytic tools discussed in this paper are being
integrated in the LetterSampo system. Code is available at
https://version.aalto.fi/gitlab/urenaj1/rofl_communication_patterns.

## References

  * [1] Lazer DM, Pentland A, Watts DJ, Aral S, Athey S, Contractor N, Freelon D, Gonzalez-Bailon S, King G, Margetts H, _et al._ 2020 Computational social science: Obstacles and opportunities.  _Science_ 369, 6507, 1060–1062.
  * [2] Lazer D, Hargittai E, Freelon D, Gonzalez-Bailon S, Munger K, Ognyanova K, Radford J. 2021 Meaningful measures of human society in the twenty-first century.  _Nature_ pp. 1–8.
  * [3] Onnela JP, Saramäki J, Hyvönen J, Szabó G, Lazer D, Kaski K, Kertész J, Barabási AL. 2007 Structure and tie strengths in mobile communication networks.  _Proceedings of the National Academy of Sciences_ 104, 18, 7332–7336.  (doi:10.1073/pnas.0610245104).
  * [4] Candia J, González MC, Wang P, Schoenharl T, Madey G, Barabási AL. 2008 Uncovering individual and collective human dynamics from mobile phone records.  _Journal of Physics A: Mathematical and Theoretical_ 41, 22, 224015.  (doi:10.1088/1751-8113/41/22/224015).
  * [5] Borgatti SP, Mehra A, Brass DJ, Labianca G. 2009 Network analysis in the social sciences.  _Science_ 323, 5916, 892–895.  (doi:10.f1126/science.1165821).
  * [6] Holme P, Saramäki J. 2012 Temporal networks.  _Physics Reports_ 519, 3, 97–125.  (doi:10.1016/j.physrep.2012.03.001).
  * [7] Miritello G. 2013 _Temporal Patterns of Communication in Social Networks_.  Springer International Publishing.  (doi:10.1007/978-3-319-00110-4).
  * [8] Miritello G, Lara R, Cebrian M, Moro E. 2013 Limited communication capacity unveils strategies for human interaction.  _Scientific Reports_ 3, 1.  (doi:10.1038/srep01950).
  * [9] Miritello G, Lara R, Moro E. 2013 Time allocation in social networks: Correlation between social structure and human communication dynamics.  In: _Understanding Complex Systems_ , pp. 175–190. Springer Berlin Heidelberg.  (doi:10.1007/978-3-642-36461-7\textunderscore9).
  * [10] Barabási A, Jeong H, Néda Z, Ravasz E, Schubert A, Vicsek T. 2002 Evolution of the social network of scientific collaborations.  _Physica A: Statistical Mechanics and its Applications_ 311, 3-4, 590–614.  (doi:10.1016/s0378-4371(02)00736-7).
  * [11] Innis H. 1951 _The Bias of Communication_.  University of Toronto Press.
  * [12] McLuhan M. 1988 The role of new media in social change.  In: G S, F M (eds.), _Marshall McLuhan: The man and his message_ , pp. 34–35. Fulcrum Inc.
  * [13] Rombach MP, Porter MA, Fowler JH, Mucha PJ. 2013 Core-periphery structure in networks.  _SSRN Electronic Journal_ (doi:10.2139/ssrn.2002684).
  * [14] Milgram S. 1967 The small-world problem.  _Psychology Today_ 1, 1.
  * [15] Karsai M, Kivelä M, Pan RK, Kaski K, Kertész J, Barabási AL, Saramäki J. 2011 Small but slow world: How network topology and burstiness slow down spreading.  _Physical Review E_ 83, 2.  (doi:10.1103/physreve.83.025102).
  * [16] Onnela JP, Saramäki J, Hyvönen J, Szabó G, Argollo de Menezes M, Kaski K, Barabási AL, Kertész J. 2007 Analysis of a large-scale weighted network of one-to-one human communications.  _New Journal of Physics_ 9, 179.
  * [17] Kivelä M, Pan RK, Kaski K, Kertész J, Saramäki J, Karsai M. 2012 Multiscale analysis of spreading in a large communication network.  _Journal of Statistical Mechanics: Theory and Experiment_ 2012, 03, P03005.  (doi:10.1088/1742-5468/2012/03/p03005).
  * [18] Saramäki J, Leicht EA, Lopez E, Roberts SGB, Reed-Tsochas F, Dunbar RIM. 2014 Persistence of social signatures in human communication.  _Proceedings of the National Academy of Sciences_ 111, 3, 942–947.  (doi:10.1073/pnas.1308540110).
  * [19] Heydari S, Roberts SG, Dunbar RIM, Saramäki J. 2018 Multichannel social signatures and persistent features of ego networks.  _Applied Network Science_ 3, 1.  (doi:10.1007/s41109-018-0065-4).
  * [20] Barabási AL. 2005 The origin of bursts and heavy tails in human dynamics.  _Nature_ 435, 7039, 207–211.  (doi:10.1038/nature03459).
  * [21] Karsai M, Kaski K, Barabási AL, Kertész J. 2012 Universal features of correlated bursty behaviour.  _Scientific Reports_ 2, 1.  (doi:10.1038/srep00397).
  * [22] Aledavood T, Lehmann S, Saramäki J. 2015 Digital daily cycles of individuals.  _Frontiers in Physics_ 3, 73.  (doi:10.3389/fphy.2015.00073).
  * [23] Lux DS, Cook HJ. 1998 Closed circles or open networks?: Communicating at a distance during the scientific revolution.  _History of Science_ 36, 2, 179–211.  (doi:10.1177/007327539803600203).
  * [24] Langmead A, Otis J, Warren C, Weingart S, Zilinski L. 2016 Towards Interoperable Network Ontologies for the Digital Humanities.  _Int. J. of Humanities and Arts Computing_ 10.  (doi:http://dx.doi.org/10.3366/ijhac.2016.0157).
  * [25] Warren CN, Shore D, Otis J, Wang L, Finegold M, Shalizi C. 2016 Six Degrees of Francis Bacon: A Statistical Method for Reconstructing Large Historical Social Networks.  _DHQ: Digital Humanities Quarterly_ 10, 3.
  * [26] van den Heuvel C. 2015 Mapping knowledge exchange in Early Modern Europe: Intellectual and technological geographies and network representations.  _International Journal of Humanities and Arts Computing_ 9, 1, 95–114.  (doi:10.3366/ijhac.2015.0140).
  * [27] van Miert D. 2016 What was the Republic of Letters? A brief introduction to a long history (1417–2008).  _Groniek_ 204/205, 269–287.
  * [28] Hotson H, Wallnig T (eds.). 2019 _Reassembling the Republic of Letters in the Digital Age_.  Göttingen University Press.
  * [29] Ravenek W, van den Heuvel C, Gerritsen G. 2017 _The ePistolarium: Origins and Techniques_ , pp. 309–316.  London: Ubiquity Press Limited.  (doi:10.5334/bbi.26).
  * [30] Daston L. 1991 The Ideal and Reality of the Republic of Letters in the Enlightenment.  _Science in Context_ 4, 2, 367–386.  (doi:10.1017/S0269889700001010).
  * [31] van den Heuvel C, Weingart SB, Spelt N, Nellen H. 2016 Circles of confidence in correspondence.  _Nuncius_ 31, 1, 78–106.  (doi:10.1163/18253911-03101002).
  * [32] van Vugt I. 2019 _The structure and dynamics of scholarly networks between the Dutch Republic and the Grand Duchy of Tuscany in the 17th Century_.  Universiteit van Amsterdam.
  * [33] Feld SL. 1981 The focused organization of social ties.  _American Journal of Sociology_ 86, 5, 1015–1035.  (doi:10.1086/227352).
  * [34] Ryan Y, Ahnert S, Ahnert R. 2020 Networking archives: Quantitative history and the contingent archive.  In: _Proceedings of the Workshop on Computational Humanities Research (CHR 2020)_ , Vol-2723.
  * [35] Ryan YC, Ahnert SE. 2021 The measure of the archive: The robustness of network analysis in early modern correspondence.  _Journal of Cultural Analytics_ (doi:10.22148/001c.25943).
  * [36] Saramäki J, Moro E. 2015 From seconds to months: an overview of multi-scale dynamics of mobile telephone calls.  _The European Physical Journal B_ 88, 6.  (doi:10.1140/epjb/e2015-60106-6).
  * [37] Ahnert R, Ahnert SE. 2015 Protestant letter networks in the reign of mary i: A quantitative approach.  _ELH_ 82, 1, 1–1.  (doi:10.1353/elh.2015.0000).
  * [38] Holme P. 2019 Rare and everywhere: Perspectives on scale-free networks.  _Nature Communications_ 10, 1.  (doi:10.1038/s41467-019-09038-8).
  * [39] Granovetter MS. 1973 The strength of weak ties.  _American Journal of Sociology_ 78, 6, 1360–1380.  (doi:10.1086/225469).
  * [40] Zeller RA, Nock SL, Carmines EG. 1982 Measurement in the social sciences: The link between theory and data.  _Contemporary Sociology_ 11, 1, 79.  (doi:10.2307/2066656).
  * [41] Ureña-Carrion J, Saramäki J, Kivelä M. 2020 Estimating tie strength in social networks using temporal communication data.  _EPJ Data Science_ 9, 1.  (doi:10.1140/epjds/s13688-020-00256-5).
  * [42] Navarro H, Miritello G, Canales A, Moro E. 2017 Temporal patterns behind the strength of persistent ties.  _EPJ Data Science_ 6, 1.  (doi:10.1140/epjds/s13688-017-0127-3).
  * [43] Goh KI, Barabási AL. 2008 Burstiness and memory in complex systems.  _EPL (Europhysics Letters)_ 81, 4, 48002.  (doi:10.1209/0295-5075/81/48002).
  * [44] Karsai M, Kaski K, Kertész J. 2012 Correlated dynamics in egocentric communication networks.  _PLoS ONE_ 7, 7, e40612.  (doi:10.1371/journal.pone.0040612).
  * [45] Malmgren RD, Stouffer DB, Motter AE, Amaral LA. 2008 A poissonian explanation for heavy tails in e-mail communication.  _Proceedings of the National Academy of Sciences_ 105, 47, 18153–18158.
  * [46] Oliveira JG, Barabási AL. 2005 Darwin and einstein correspondence patterns.  _Nature_ 437, 7063, 1251–1251.  (doi:10.1038/4371251a).
  * [47] Malmgren RD, Stouffer DB, Campanharo ASLO, Amaral LAN. 2009 On universality in human correspondence activity.  _Science_ 325, 5948, 1696–1700.  (doi:10.1126/science.1174562).
  * [48] Colavizza G. 2014 _Mapping early modern news networks: a digital humanities approach_.  Master’s thesis, Università Ca’ Foscari Venezia.  (doi:10.13140/RG.2.2.26344.88326).  Http://hdl.handle.net/10579/4893.
  * [49] Dooley B (ed.). 2010 _The Dissemination of News and the Emergence of Contemporaneity in Early Modern Europe_.  Ashgate Farham.  (doi:10.4324/9781315240244).
  * [50] Viswanath B, Mislove A, Cha M, Gummadi KP. 2009 On the evolution of user interaction in Facebook.  In: _Proceedings of the 2nd ACM workshop on Online social networks - WOSN 09_. ACM Press.  (doi:10.1145/1592665.1592675).
  * [51] Rossi RA, Ahmed NK. 2015 The network data repository with interactive graph analytics and visualization.  In: _AAAI_.
  * [52] Karimi F, Ramenzoni VC, Holme P. 2014 Structural differences between open and direct communication in an online community.  _Physica A: Statistical Mechanics and its Applications_ 414, 263–273.  (doi:10.1016/j.physa.2014.07.037).
  * [53] Dumont S. 2016 correspSearch –– Connecting Scholarly Editions of Letters.  _Journal of the Text Encoding Initiative_ 6, 10.  (doi:10.4000/jtei.1742).
  * [54] Hyvönen E, Tuominen J, Alonen M, Mäkelä E. 2014 Linked Data Finland: A 7-star model and platform for publishing and re-using linked datasets.  In: _The Semantic Web: ESWC 2014 Satellite Events, Revised Selected Papers_ , pp. 226–230. Springer-Verlag.
  * [55] Heath T, Bizer C. 2011 _Linked Data: Evolving the Web into a Global Data Space_.  Synthesis Lectures on the Semantic Web: Theory and Technology. Morgan & Claypool.
  * [56] Kivelä M, Porter MA. 2015 Estimating interevent time distributions from finite observation periods in communication networks.  _Physical Review E_ 92, 5.  (doi:10.1103/physreve.92.052813).
  * [57] Hyvönen E, Leskinen P, Tuominen J. 2020.  From the Republic of Letters to LetterSampo – Historical Letters on the Semantic Web.  White paper, Aalto University, Semantic Computing Research Group (SeCo): https://seco.cs.aalto.fi/publications/2020/hyvonen-et-al-lettersampo-2020.pdf.
  * [58] Leskinen P, Ureña-Carrion J, Tuominen J, Kivelä M, Hyvönen E.  Using a linked data service for analysing temporal communication networks – applications to emails and historical letters.  White paper, Aalto University, Semantic Computing Research Group (SeCo).
  * [59] Hyvönen E. 2020 "Sampo" model and semantic portals for digital humanities on the semantic web.  In: _DHN 2020 Digital Humanities in the Nordic Countries. Proceedings of the Digital Humanities in the Nordic Countries 5th Conference_ , pp. 373–378. CEUR Workshop Proceedings, vol. 2612.