Methods Ecol Evol. 2020;00:1–12. wileyonlinelibrary.com/journal/mee3
1© 2020 British Ecological Society
1 | INTRODUCTION
For those unfamiliar with social network analysis (SNA) terminol-
ogy (highlighted in the text with asterisks), we provide a glossar y in
Table 1. The mathematical formulae of all the network measures dis-
cussed in this manuscript are provided in Appendix S1 and software
handling their computation are in Appendix S2.
Social network analysis has become a methodological framework
that allows a transdisciplinary approach (from proteomic research
to animal societies and ecosystems) to study multiple questions
within single systems (networks*) such as groups, populations as
well as connected units (links* and nodes*) of the systems. For ex-
ample, in the study of animal societies, SNA can reveal the causes
and consequences of individuals’ social heterogeneity (variation in
social behaviour) and link the social interactions to both ecological
and evolutionary processes (Sueur, Romano, Sosa, & Puga-Gonzalez,
2019). Here we describe how the use of specific network measures*
can lead to study these different aspects and levels.
The surge of SNA in the last couple of decades has been ac-
companied by the development of a large number of analytical
software and methods to calculate network measures (Borgatti,
Everett, & Freeman, 20 02; Csardi & Nepusz, 2006; Sosa et al., 2018;
Whitehead, 2009). This has resulted in a diversity of software that
vary in the way some network measures are calculated (because
they used different methods), and/or are specialized in calculations/
functions designed with a specific research purpose, here referred to
as variant s. Not surprisingly, non-exper ts in SNA may find dif ficult to
get a clear picture of the most adequate approaches or tools for their
In this manuscript, we do not aim to show the usefulness of SNA
(which was already proved many times); instead we provide the
reader with an extensive list of the different measures* (and their
variants) that are commonly used in animal social network analysis
(ASNA) for static networks or time-aggregated networks. We do so
to highlight how mathematical dif ferences in the calculation of these
measurements may af fect the interpretation of results, making it
necessary to indicate some considerations that have not been taken
so far. Our aim was to provide researchers with a guideline that
helps them to: (a) interpret the different measures and their variants,
(b) choose a specific measure according to the research question
and (c) avoid misuses of SNA measures. Although we provide a pre-
scriptive approach on which network measure to use, when and how
Received: 24 September 2019
Accepted: 3 January 2020
DOI : 10.1111 /20 41-210X.1336 6
ANIMAL SOCIAL NETWORKS
Network measures in animal social network analysis:
Their strengths, limits, interpretations and uses
Sebastian Sosa1 | Cédric Sueur1,2 | Ivan Puga-Gonzalez3
1Universi té de Strasbourg , CNRS, IPHC UMR
7178, Strasbourg, France
2Instit ut Univer sitaire de France , Paris,
3Institute for Global Development and
Plannin g, University of A gder, Kristiansand,
Handling Editor: Timothée Poisot
1. We provide an overview of the most commonly used social network measures in
animal research for static networks or time-aggregated networks.
2. For each of these measures, we provide clear explanations as to what they meas-
ure, we describe their respective variants, we underline the necessity to consider
these variants according to the research question addressed, and we indicate con-
siderations that have not been taken so far.
3. We provide a guideline indicating how to use them depending on the data col-
lection protocol, the social system studied and the research question addressed.
Finally, we inform about the existent gaps and remaining challenges in the use of
several variants and provide future research directions.
animal research, animal social networks, net work measures, social network analysis, social
network measures, static networks, time-aggregated networks
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SOSA et Al .
depending on the research question, the data collection protocol
and the species-specific social structure (Figures 1‒3), readers may
keep in mind that SNA is a versatile tool and each research question
and system requires its own, bespoke set of considerations to deal
with its own specificities.
1.1 | Considerations prior to selecting
Before considering the computation of net work measures, one
may first consider the type of data collected (e.g. rare or frequent,
associations or interactions), the type of system under study
(e.g. cohesive social group, population, etc.), the environment in
which individuals evolve (e.g. forest or open field) and how the
data are collected (e.g. scan sampling, focal sampling, gambit of
the group [GoG]) as each of these fac tors may affect the accu-
racy of the data collected and the extent to which the data are a
fair representation of the system. For example, data collected in
animal social research can be divided into two main categories,
namely associations and interactions. Associations are usually col-
lected with GoG or scan sampling and interactions with scan or
focal samplings. Whereas GoG allows to rapidly collect numer-
ous individual associations, it inevitably generates networks with
Ter m s Definition
Alters Nodes connected to ego
Binary Considering the presence or absence of links between two
Closed triplets Three nodes interconnected between each other
Directed network Network with link directionality (representing the directionalit y
of the behaviour)
Directionality Link directionality from one node to another
Ego A specific node
Ego-network A network with ego's connections only
Incoming links Interaction received
Link Element of a network representing the connection
(e.g. interaction or association) between two nodes. Term edge
is used as synonym in the literature
Micro-motifs Substructures of a network
Network A system of interconnected elements
Network clusterization Formation of subgroups in a network
Network global measures Measures calculated at the level of the whole network
Network measures Mathematical calculations to quantify specific features of a
network, inclu de global, node and polyadic measures
Network node measures Measures calculated at the level of nodes
Network resilience Capacity for the network to remain undisrupted when nodes are
How well pathogens or information spread in the net work
Node Element of a network representing an individual. Term vertice is
used as synonym in the literature
Node centrality A central node is highly connected and/or is connected to highly
Outgoing links Interaction given
Strongest links Links with highest weights
Undirected network Network without link directionality
Unweighted network Networ k in which links represent the presence (1) or absence (0)
of interactions/associations between nodes
Weakest links Links with lowest weights
Weigh t Value of a link usually representing the frequenc y of an
Weighted network Network in which the weights of the links represent the
frequency of interactions/associations between nodes
TABLE 1 Network glossary
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SOSA et Al .
higher density than networks based on social interactions that
are generally distributed differently depending on the social part-
ners as well as undirected* networks (Franks, Ruxton, & James,
2010). This aspect entails the following three main considerations:
(a) whether network associations represent faithfully the group/
population social structure, (b) the usefulness of GoG in the study
of social dif fusion such as epidemiology and (c) the use of meas-
ures that do not consider links’ weights* in networks obtained
through GoG. Similarly, the system studied and the environment in
which individuals evolve may make it necessar y to adapt the data
collection protocol. For example, scan sampling can be perfectly
adapted for the study of cohesive species with a well-known
group composition, small size and/or living in an open environ-
ment whereas focal sampling may be preferred for larger cohesive
species living in dense forests or fission-fusion societies (in this
case, scan sampling may lead to oversample the core group easily
visible). As a rule, one may consider that it is not the best choice to
use data obtained through GoG for the study of social diffusion or
the computation of measures that do not consider links’ weights as
this observation protocol produces highly dense networks and the
link filtering usually performed to reduce the density generates
important biases (Franks et al., 2010).
FIGURE 1 Decision tree for examining individual social heterogeneity according to the research question and the network studied
FIGURE 2 Decision tree for examining patterns of individual interactions according to the research question and the network studied
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SOSA et Al .
1.2 | Examining heterogeneity in node interactions
Node measures* (Figure 1) enable to assess individuals’ social hetero-
geneity and to understand the underlying mechanisms such as indi-
vidual characteristics (e.g. ageing process; Almeling, Hammerschmidt,
Sennhenn-Reulen, Freund, & Fischer, 2016), ecological factors
(e.g. demographic variation; Borgeaud, Sosa, Sueur, & Bshary, 2017)
and evolutionary processes (e.g. differences in social st yles; Sueur
et al., 2011). Node measures are calculated at an individual level and
assess in d ifferent ways and wi th different mea nings how an indivi dual
is connected. Connections can be ego's* direct links only (e.g. degree,
streng th), alters’* links as well (e.g. eigenvector, clustering coeffi-
cient) or even all the links of the network (e.g. betweenness). Node
measures can also be used to describe the overall network structure
through distributions, means and coefficients of variation.
1.2.1 | Degree and strength
The degree measures the number of links of a node. When computed
on an undirected network, the degree represents the number of alters
of ego. When the network is directed*, it represents the number of
either incoming* or outgoing* links of ego and it is then called in-
degree (i.e. number of incoming links) or out-degree (i.e. number of
outgoing links) respectively. In-degree is generally used as a measure
of popularity in affiliative networks and out-degree as a measure of
expansiveness (Borgatti, Everett, & Johnson, 2018). Note that degree
can also be computed in directed networks, in this case it represents
the sum of incoming and outgoing links and not the number of alters.
Strength (or weighted degree) is the sum of links’ weights in a
weighted network*. When the network comprises direc ted links,
then it is also possible to differentiate bet ween in-strength (the sum
of weights of incoming links) and out-strength (the sum of weights
of outgoing links). In ASNA, these measures usually represent the
frequency of individuals’ interactions/associations and thus reflect
individuals’ sociality and social activity. While degree and strength
can be considered correlated, it may not always be the case as indi-
viduals can interact frequently with few social partners or vice versa
(Liao, Sosa, Wu, & Zhang, 2018). Therefore, it is necessary to test
their correlation prior to the analysis.
There is a long list of research that have used degree and
streng th; these are the main findings: Degree has been found to
decrease with age in primates and marmots (Almeling et al., 2016)
while strength does not (Almeling et al., 2016; Liao et al., 2018).
The philopatric sex has shown higher affiliative degree and affil-
iative strength in several species (Borgeaud, et al., 2017) as well
as high-ranked individuals (Brent, Ruiz-Lambides, & Platt, 2017b).
A positive correlation has been found between parasite load and
degree and streng th (Leu, Farine, Wey, Sih, & Bull, 2016), although
this correlation may be compensated by social buffering/suppor t
(Scharf, Modlmeier, Beros, & Foitzik, 2012). Several personality
traits have been positively related to degree and strength such
as exploration (Aplin, Farine, Mann, & Sheldon, 2014) or boldness
(Moyers, Adelman, Farine, Moore, & Hawley, 2018). In several
FIGURE 3 Decision tree for examining group structure and properties according to the research question and the network studied
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primate species, the social circle of infants (i.e. mothers’ degrees)
has been found to have a significant impact on their develop-
ment (Shimada & Sueur, 2014). Finally, individuals with wider so-
cial circles show higher longevit y (Brent, Ruiz-Lambides, & Plat t,
2017a; Silk et al., 2010) and greater reproductive success (Schülke,
Bhagavatula, Vigilant, & Ostner, 2010).
Degree shows low sensitivity to observation biases (e.g. misiden-
tification of individuals or unobserved interactions), which makes it
particularly relevant for epidemiology studies (Krause, James, Franks,
& Croft, 2014). However, when considering data collection, due to
the high connectiveness of networks generated by GoG, degree may
be less suitable than strength since degree is strongly correlated with
density. Finally, cautions must be taken when using software as the
computation of degree with directed networks induces by default the
computation of the sum of incoming and outgoing links and not the
number of alters. These contrasting variants of a measure as simple as
the degree serve as a reminder that special care must be taken as to
the mathematical formulae applied to avoid misinterpretations.
1.2.2 | Eigenvector centrality
Eigenvector centrality is the first non-negative eigenvector value
obtained by transforming an adjacency matrix linearly. It can be
computed on weighted, binary*, directed or undirected networks.
It measures the centrality* by examining the connectedness of ego
as well as that of its alters. Thus, a node's eigenvector value can
be linked either to its own degree or strength or to the degrees or
streng ths of the nodes to which it is connected.
Eigenvector may be interpreted as the social support or social
capital of an individual (Brent, Semple, Dubuc, Heistermann, &
MacLarnon, 2011), that is the real or perceived availability of so-
cial resources. Eigenvector has been extensively used in ASNA and
is linked to biological aspects such as individual fitness (Stanton &
Mann, 2012), epidemiology (Balasubramaniam, Beisner, Vandeleest,
Atwill, & McCowan, 2016), individual characteristics (Sosa, 2016) or
social st yle (Sueur et al., 2011).
1.2.3 | Betweenness
Betweenness is the number of times a node is included in the short-
est paths (geodesic distances) generated by every combination of
two nodes. The value of the bet weenness informs on the theoretical
role of a node in the social transmission (information, disease, etc.,
see Figure 1) as it indicates to what extent a node connect s sub-
groups, as a bridge, and then is likely to spread an entity across the
whole network (Newman, 2005).
To date, betweenness has been related to network cohesion
(Lusseau & Newman, 20 04), infection processes (Balasubramaniam
et al., 2016), information transmission (Pasquaretta et al., 2016), sex
(Zhang, Li, Qi, MacIntosh, & Watanabe, 2012), age, rank, kinship
(Bret et al., 2013) and fitness (Gilby et al., 2013). Nodes with the
highest betweenness usually link clusters/modules of nodes within
the networks (e.g. different subgroups or populations) and may thus
have an impor tant role in group cohesion or exchange of entities
(disease, information, genes). However, betweenness is not always
the most informative network measure for an individual's role in
disease spread and such variation could be related to the network
structure (Rodrigues, 2019).
Special attention must be paid regarding the calculation of the
betweenness since the way it is calculated depends on whether
the network is binary or weighted, direc ted or undirected and on
whether the lowest or the highest link/relationship strength is in-
terpreted as the shortest path. Therefore, the different calculations
may lead to dif ferent values. Fur thermore, bet weenness seems to be
very sensitive to sampling effort (Krause et al., 2014).
Closeness is another well-known network measure to study node
centrality but we do not discuss it here as it is ver y similar—although
less frequently used—to betweenness (same variants, same consider-
ations required), and betweenness is usually preferred in ASNA.
1.2.4 | Local clustering coefficient
The local clustering coefficient measures the number of closed tri-
plets* over the total theoretical number of triplets (i.e. open and
closed), where a triplet is an ensemble of three nodes that are con-
nected by either two (open triplet) or three (closed triplet) edges.
This measure aims to examine the links that may exist between the
alters of ego and measures the cohesion of the network (Figure 1).
The main topological effect of closed triplets is the clusterization of
the network, generating cohesive clusters, and is thus strongly re-
lated to modularity (see corresponding section). The local clustering
coefficient can be computed in a binary network by measuring the
proportion of links between the nodes of an ego-network* divided by
the number of potential links between them. In weighted networks,
several versions exist such as those from Barrat, Barthelemy, Pastor-
Satorras, and Vespignani (2004) or Opsahl and Panzarasa (2009). To
date, no attempt has been made in ASNA to evaluate which version
of the clustering coefficient may be the most appropriate accord-
ing to the research question. Therefore, careful attention is needed
when choosing the variant as this may lead to different biological
interpretations. For example, Opsahl's generalized clustering coef-
ficient proposes four variants to consider triplets’ link weights (the
arithmetic or geometric mean or using the weight of the weakest*
or strongest* links). Opsahl's geometric mean variant considers tri-
plet weights heterogeneity (and is robust against extreme values of
weights) whereas Barrat's variant does not. Thus, heterogeneity of
weights should be preferred in social systems with high social het-
erogeneity such as groups with high hierarchy steepness for example.
Finally, the minimum variant (using the weight of the weakest link in
a closed triplet) should be preferred when trying to understand the
mechanisms that shape link creation in animal societies since this
variant helps determine the minimum threshold needed for closed
triplets to appear.
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One major asset of this measure is that it is both local and global,
which allows to examine for example how such micro-motifs* affect
the overall network structure (Wharrie, Azizi, & Altmann, 2019). As
we will see, the clustering coefficient examines different aspects of
social networks and animal societies, going from individual hetero-
geneity of social interactions (present section) to the analysis of the
overall group structure (see Global clustering coefficient) and it also
explains patterns in links’ creation (see Transitive triplets). However,
the local and global clustering coefficients can be importantly re-
lated to density so both measures require special attention when
data are collected through GoG and, additionally, density should be
added as factor of control.
1.3 | Examining patterns of node interactions
Patterns of interac tions (how and with whom individuals interact)
can be examined using specific network measures* that analyse
local-scale interactions within a network and make possible to test
hypotheses about the mechanisms underlying network connectiv-
ity (Figure 2). These types of measures are generally used to test
mechanistic biological questions, such as what factors (e.g. eco-
logical as well as sociodemographic) affect individuals’ interactions/
associations. However, because these patterns of interactions are
also known to affect global network features, such as group resil-
ience or reciprocal interactions, and to occur in a wide variet y of ani-
mal taxa, they may be crucial elements within the general processes
that shape animal societies and populations.
1.3.1 | Assortativity
Assor tativity (Newman, 2003) is probably the most used measure
to study homophily (preferential associations or interactions among
individuals sharing the same characteristics; Lazarsfeld & Merton,
1954). Assortativity values range from −1 (total disassortativity
i.e. all the nodes associate or interact with those with the opposite
characteristic, such as males interacting exclusively with females)
to 1 (total assortativity i.e. all the nodes associate or interact with
those with the same characteristic such as males interacting only
with males). The assor tativity coef ficient measures the proportion
of links between and within clusters of nodes with same characteris-
tics. Individuals’ characteristics can be continuous (e.g. age, individ-
ual network measure, personality) or categorical features (e.g. sex,
matriline belonging; Figure 2). Assortativity does not consider direc-
tionalit y* and can be measured in weighted (Leung & Chau, 2007)
or binary (Newman, 2003) networks using categorical or continu-
ous characteristics (Figure 2). The use of one or other assortativit y
variant depends on the type of characteristics being examined and,
whenever possible, the weighted version should be preferred since it
is more reliable than the binary version (Farine, 2014).
Recent studies in human research argue that homophily promotes
cooperation, social learning, and cultural and norm transmission among
strangers (Allen, Weinrich, Hoppitt, & Rendell, 2013). Homophily ac-
cording to different phenotypes such as sex, age, kinship, hierarchical
rank (Sosa, 2016), degree (Croft et al., 2005), personality (Croft et al.,
2009) or body size (Leu et al., 2016) has been found in several species
inc luding fish (Crof t et al., 200 5), birds (Johnso n et al ., 2017), cet acean s
(Hunt, Allen, Bejder, & Parra, 2019), humans (Wang, Suri, & Watts,
2012) and other mammals ( Williamson, Franks, & Curley, 2016). The
fact that similar homophilic mechanisms are found in a wide range of
taxa suggests that homophily may have been a driver for cooperation
between congeners (Apicella, Marlowe, Fowler, & Christakis, 2012).
One question that remains open, however, is whether assortativity is a
consequence of evolution or a prior condition for cooperation, which
would need to be investigated fur ther.
1.3.2 | Transitive triplets
Transitive triplets are micro-motifs that have widely been widely ex-
amined in ASNA in recent years. Transitive triplets are closed triplets
where the links among the nodes follow a specific temporal pattern
of creation, that is when the establishment of links between nodes
A and B and between nodes A and C is followed by the establish-
ment of a link between nodes B and C. This network measure can
be computed in directed, binary or weighted networks. This type
of connections can be studied over time based on the creation of
links. From a static perspec tive, directionality can be considered by
calculating the number of transitive triplets divided by the number
of potential transitive triplets, and weights can also be considered by
using Opsahls’ variants, which are discussed in the section on local
clustering coefficient (Opsahl & Panzarasa, 2009). While transitiv-
ity is importantly related to the clustering coefficient (the clustering
coefficient includes transitive triplets), not all close triplets are tran-
sitive. Transitive triplets are one of the 16 possible configurations of
a triplet considering open and closed triplets as well as link direction-
ality (i.e. triad census).
Transitive triplets have been used in animal affiliative social net-
works (Borgeaud, Sosa, Bshary, Sueur, & Waal, 2016; Boucherie,
Sosa, Pasquaret ta, & Dufour, 2016; Ilany, Booms, & Holekamp, 2015;
Sosa, Zhang, & Cabanes, 2017; Waters & Fewell, 2012) to highlight
‘triadic closure’, commonly described as ‘the friend of my friend is
my friend’. Ilany et al. (2015) evidenced that several factors (rainfall,
prey availability, sex, social rank, dispersal status and topological ef-
fects) shape social dynamics in wild hyenas. Among all these factors,
transitive triplets appeared as the most consistent and social dynam-
ics (link creation) could not be explained without it. This micro-motif
represents an interesting measure when studying social network
resiliency and efficiency. For example, in ants, transitive triplets
appear supporting the hypothesis of adapted and selected pat-
terns of interactions to increase colony functionality and efficiency
(Waters & Fewell, 2012). Moreover, the main topological effect of
triadic closure is the clusterization of the network generating cohe-
sive groups and it seems to be closely linked to the emergence of
reciprocity, altruism and cooperation (Davidsen, Ebel, & Bornholdt,
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SOSA et Al .
2002). As for assor tativity, studies testing how this micro-motif
affects the spread of information could help gain knowledge on this
crucial mechanism in the evolution of animal societies.
Transitive triplets have also been used to study agonistic networks
and animals’ dominance hierarchy. For instance, the study of Dey and
Quinn (2014) showed that pukeko agonistic net works emerge from
both individual characteristics and endogenous self-organization of
dominance relationships (i.e. transitive triplets). While triad census has
not been widely used in the past, few studies have started to use these
micro-motifs to examine hierarchy linearity on the basis of occurrence
of reciprocal triplets for example (Shizuka & McDonald, 2012).
Transitive triplets, and triad census more generally, help to
understand how relationships between individuals emerge and
change over time and how these changes may be a consequence of
changes in others’ relationships (Figure 2). The studies mentioned
above investigated triplets’ configuration using unweighted* net-
works. While the weighted variant of transitive triplets (Opsahl &
Panzarasa, 2009) may allow researchers to better understand and
predict how and when links bet ween two individuals are created, it
remains unused in ASNA to date.
1.4 | Examining network structure and properties
The structure of this section is based on the distinction between
network connectivity and social diffusion (information or disease
spread). Both of these aspects may overlap the use of the network
measures that quantify the m (Figure 3). However, the social d iffusion
section contains measures specifically designed to study theoretical
(i.e. considering the diffusion is perfectly related to network links
and link weights) social diffusion features based on the geodesic
distances (see corresponding section). Aspects of the struc ture and
proper ties of a group (e.g. cohesion, sub-grouping) can be quanti-
fied using global network measures*. For instance, one may quantify
proper ties such as network resilience* (see Diameter), network clus-
terization* (see Modularity) through network connectivity analysis,
or network transmission efficiency* (see Global efficienc y) through
network theoretical social diffusion analysis (Figure 3). These differ-
ent network structures have been used in ASNA to study dif ferent
evolutionary as how the network is structured, resilient or efficient
(Puga-Gonzalez, Sosa, & Sueur, 2018) and ecological questions as
how ecological factors such as pathogens affect the network struc-
ture (Croft et al., 2011).
1.4.1 | Examining network connectivity
Network connectivity can be studied using global network meas-
ures that describe the cohesion of the network and how this cohe-
sion may be affected by intrinsic (e.g. species social organization and
structure) or extrinsic factors (e.g. ecological factors as pathogens).
There are three main measures for connectivity discussed in this sec-
tion: density, modularity and clustering coefficient. A s mentioned
above, all these measures may affect social diffusion as high density
and clustering coef ficient induce a fast rate whereas high modularit y
induces a low rate of spread.
The density is the ratio between existing links and all potential links
of a network. This measure is easy to interpret, it assesses how a
network is fully connected. Density does not consider directionality
neither link weights.
In ASNA , a link has been found between density and factors
such as living condition (i.e. higher densit y in captive groups than
in wild groups), group size (i.e. Balasubramaniam et al., 2017; with
the larger the group, the lower the density), seasonality (i.e. higher
density during the mating season; Brent, MacLarnon, Platt, &
Semple, 2013), habitat structural complexity (i.e. higher density
in complex habitats; Leu et al., 2016) and population stress due
to environmental changes (Dufour, Sueur, Whiten, & Buchanan-
However, cautions should be taken when studying density
since this measure may depend on the biology of the species (e.g.
social system and group size) and because several other network
measures appear correlated with it. Density is correlated with de-
gree distribution (see corresponding section), geodesic distances
(see corresponding section) and the frequency of micro-motifs,
like closed triplets* and thus clustering coefficients (see corre-
sponding section; Rankin et al., 2016). These correlations between
density and other global net work measures make it necessar y to
control for network density when comparing global network mea-
sures from different groups, conditions or species. Furthermore,
when comparing species, special attention should be put that the
social organizations (e.g. group size, sex ratio) are equivalent and
thus that interspecies comparisons are meaningful. Furthermore,
the type of behaviour (the rarer the behaviour, the lower the den-
sity; Castles et al., 2014), the size of the network and the sampling
effort are other factors that may influence density and should be
taken into consideration when comparing networks. Methods to
control for such biases have already been proposed (e.g. evalua-
tion of the data collec tion robustness) and should be used when-
ever differences in global network measures (density or other
ones) are assessed (Balasubramaniam et al., 2017). Another option
is to use weighted network measures that are theoretically less
correlated with network density.
Modularity is a measure designed to quantify the degree to which
a network could be divided into different groups or clusters and its
value ranges from 0 to 1. Networks with high modularity have dense
connections within the modules but sparse connections between
the modules. Modularity can be computed in weighted, binar y, di-
rected or undirected networks.
It has been evidenced that modularity varies according to dom-
inance st yle in macaque species, with higher modularity found
in despotic species (Sueur et al. 2011). Fission–fusion societies as
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SOSA et Al .
elephants (Wittemyer & Getz, 2007), geladas (Matsuda et al., 2015)
or snub-nosed monkeys (Zhang et al., 2012) show many units and
thus high modularity compared to cohesive groups. Modularity also
seems to be linked to evolutionary advantages such as greater co-
operation by the creation of clusters of cooperators (Marcoux &
Lusseau, 2013) or reduced risks of transmission of pathogens by
decreasing associations between clusters (Nunn, Jordán, McCabe,
Verdolin, & Fewell, 2015). Individuals that interlink the different
clusters may be those with specific social status as observed in dol-
phins (Lusseau & Conradt, 20 09) but clusters can also be linked by
weak links that allow to maintain a certain cohesion and social trans-
mission as described in giraffes (VanderWaal et al., 2016).
Several algorithms have been proposed to identify the different
clusters in a network. These can be categorized according to the
process used to identify the clusters such as spectral optimization
(leading eigenvector), based on the struc ture of the edges (edge be-
tweenness), or modularity optimization (Fastgreedy or Louvain algo-
rithm). For an overview, see Yang, Algesheimer, and Tessone (2016).
Until recently, no research had investigated what would be the im-
pact of choosing different community detection algorithms in the
results (Aldecoa & Marín, 2013; Sumner, McCabe, & Nunn, 2018).
Sumner et al. (2018) showed possible variations between those dif-
ferent algorithms; therefore, we recommend to choose carefully an
appropriate community detection algorithm for the question of in-
terest. Unfortunately, it is only recently that these questions have
been addressed and a general guideline cannot be provided except
that multiple algorithms may be used and the results may be com-
pared. Also note that such precautions could apply to any clusteri-
Global clustering coefficient
The global clustering coefficient, like the local clustering coeffi-
cient, evaluates how well the alters of ego are interconnected and
measures the cohesion of the network. It s main topological effect
is the clusterization of the network, generating cohesive clusters,
and is thus strongly related to modularit y. However, it becomes
highly correlated with density and less to modularity as the den-
sity grows. Several variants of the global clustering coefficient can
be found: (a) the ratio of closed triplets to all triplets (open and
closed), (b) the binary local mean clustering coef ficient that de-
rives from the node level (see Local clustering coefficient). The
binary local mean clustering coefficient allows to consider node
heterogeneity and thus should be preferred over the first variant.
Weighted versions also exist and are based on the same variants
described in the section on the local clustering coefficient and re-
quire the same considerations.
1.4.2 | Examining social diffusion
One major aspect that SNA brings in the study of social struc ture is the
possibility to examine social diffusion of disease, information transmis-
sion, new behaviour or ecosystems’ food flow in a network (Figure 3).
One of the measures that make this possible is the geodesic distance
and derived measures such as global efficiency and diameter. While
geodesic distance is not often used in ASNA, it is essential for calculat-
ing other network measures such as diameter, global efficiency, node
betweenness (see corresponding sections). Therefore, we discuss geo-
desic distance in this section to inform the reader that the cautions
needed when computing geodesic distances must also be considered
when calculating its derived network measures.
Geodesic distance is the shortest path considering all potential
dyads in a network. This measure thereby evidences the fastest path
of diffusion. Despite its usefulness in the study of epidemiology,
geodesic distance remains seldomly used in ASNA due to its high
sensitivity to observation biases such as unobserved interactions or
misidentification of individuals (Krause et al., 2014). Geodesic dis-
tance can be calculated in binary, weighted*, directed or undirected
networks. In weighted networks, it can be normalized (by dividing all
links by the network weight means) and the strongest or the weakest
links can be considered as the fastest route between two nodes. This
great number of variants of geodesic distance can greatly affect the
results and interpretations. Researchers must thus have knowledge
of the variants and which one is the most appropriate according to
their research question (Opsahl, Agneessens, & Skvoretz, 2010).
For example, many software calculate the geodesic distance
using the paths with the lowest weights as the shortest paths be-
cause they were designed for research related to transportation
routes or information transmission (e.g. road transportation or
internet connection). However, in ASNA, the links with the high-
est weight s are usually those of greater interest as they represent
preferential interactions/associations. For example, the probability
to learn a new behaviour may be higher between individuals that
are more frequently in contact or close proximity (Hoppitt & Laland,
2013). Yet, the weakest links can also be of interest for questions
related to epidemiology. For example, although a pathogen is more
likely to be transmitted among individuals sharing strong links, weak
links may still play a role in disease transmission (VanderWaal et al.,
2016). Directionality is also an important variant to consider when
examining if diffusion can only follow a certain directionality such
as pathogens that can be transmitted only by individuals carrying it.
Global ef ficiency is the ratio between the number of individuals and
the number of connections multiplied by the network diameter. It
provides a quantitative measure of how efficiently information is ex-
changed within the nodes of the network. As global efficiency gives
a probability of social diffusion, it may help better understand so-
cial transmission phenomena in short-term and long-term (Migliano
et al., 2017). Pasquaretta et al. (2014) found a positive correlation
between the neocortex ratio and the global efficiency in primate
species with a higher neocortex ratio. By drawing a parallel between
cognitive capacities and social network efficiency, this study evi-
denced that in species with higher neocor tex ratio, individuals may
Methods in Ecology and Evoluon
SOSA et Al .
adjust their social relationships in order to gain better access to so-
cial information and thus optimize network efficiency. Alternatively,
studies on epidemiology in ant colonies showed that ants adapt their
interaction rate to decrease the network efficiency when infected
by a pathogen (Stroeymey t et al., 2018).
The diameter of a network represents the longest path of the short-
est paths in the network. Diameter is used in ASNA to examine the
aspects such as network cohesion, the rapidness of information or
disease transmission. While global efficiency measures the theoreti-
cal social diffusion spread, diameter informs on the maximum paths
of diffusion to reach all nodes.
While diameter was first used in the social sciences to study
information diffusion (Milgram, 1967), in ASNA it is mostly used
to examine social cohesion, and the resilience of the net work co-
hesion to the removal of a certain amount of central individuals
(Lusseau, 2003; Manno, 2008; Sosa, 2014; Williams & Lusseau,
2006). However, further investigation may be needed to test if the
removal of central individuals gives a fair picture of biological group
resilience proper ties since currently these analyses do not account
for the creation of new links after the loss of individuals and de-
mographic variations (Firth et al., 2017). If future outcomes support
this deletion simulation assumption, studies based on a comparative
analysis may represent an interesting research approach to under-
stand how natural selection may have favoured resilience properties
in some species while it has not in others. For example, we could
expect variation according to group structure (higher resilience in
stable matriline groups than in fusion–fission societies). Moreover,
given the insight that these simulations could provide into group or
ecosystem resilience properties, those may be of great interest for
conservation purposes (Delmas et al., 2019).
2 | DISCUSSION
This updated overview of the most commonly used network meas-
ures in ASNA highlights the increasing prominence of techniques
deriving from graph theor y, as well as the insights they brought and
their diversity. Some of these techniques were developed in specific
contexts and for well-defined questions (e.g. Latora & Marchiori,
2001 about global efficiency in neurology). It is very appealing to
reuse them with different focus although this would require a thor-
ough understanding of the mathematical background in order to
know what is being measured and to decide whether a given meas-
ure applies or not to the question raised.
We hope that this non-exhaustive overview will contribute to
facilitate future research in ASNA by helping investigators select
the most relevant network measure and variant according to their
research question. Moreover, we would like to point out that when
using SNA , one is often led to test multiple measures for a single re-
search question as these may reveal different aspects of individuals’
socialit y (direct or indirect links for example). However, it is worth
mentioning that all these measures are computed from the same
mathematical object (the network) and can therefore be correlated
(Bounova & De Weck, 2012). This correlation may be low or high
according to different parameters affecting the network, as the spe-
cies social system or organization, its size, etc. While this has been
discussed punctually along the manuscript, we cannot detail here all
the possible autocorrelations between network measures as this is
case-specific and would fall out of the scope. Nonetheless, we may
recommend to run correlation tests prior to the analyses or to use
the variance inflated factor to control for such bias in correlation
Continuous advances in graph theory such as graph signal pro-
cessing (Shuman, Narang, Frossard, Ortega, & Vandergheynst, 2013)
or multi-layer networks (Kivelä et al., 2014) will undoubtedly give
rise to novel measures with new applications in ASNA . With this per-
spective in mind, investigators need to make constant effor t testing
different versions of measures, clearly stating the mathematical in-
terpretations and what is exac tly being measured, expounding their
streng ths and limits and explaining why chose this variant rather
than another in order for others to apprehend their relevance de-
pending on the context.
We would like to thank Vincent Viblanc and reviewers from Methods
in Ecology and Evolution whose useful comments have substantially
enhanced the qualit y of the manuscript.
S.S. listed all metrics’ variants and wrote the first draft of the manu-
script; I.P.-G. and C.S. participated in the writing of the final version.
DATA AVAIL ABI LIT Y S TATEM ENT
This manuscript does not contain any data or code.
Sebastian Sosa https://orcid.org/0000-0002-5087-9135
Cédric Sueur https://orcid.org/0000-0001-8206-2739
Ivan Puga-Gonzalez https://orcid.org/0000-0003-2510-6760
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Additional suppor ting information may be found online in the
Supporting Information section.
How to cite this article: Sosa S, Sueur C, Puga-Gonzalez I.
Network measures in animal social network analysis: Their
strengths, limits, interpretations and uses. Methods Ecol Evol.
2020;00:1–12. htt ps://doi.org/10 .1111/2 041-210X.1336 6