Conceptual representations of animal social networks: an overview

Networks are now widely used to represent, quantify and model animal behaviour. These approaches have proved valuable in linking individual behaviours to emergent population level patterns and quantifying the implications of these population structures for wider ecological and evolutionary pro- cesses. However, there are diverse conceptual representations of network data and choosing the right tool to answer a particular question can be challenging. Here I provide an overview of different network representations, highlighting their potential applications in behavioural ecology and drawing attention to key resources to help with their implementation. My aim is to provide an accessible guide that helps behavioural ecologists take full advantage of the potential of the different ways in which their data can be used to generate social other networks. © 2023 The Author. Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour. This is an open access article under the CC BY license (http://creativecommons.org/licenses/ by/4.0/).

However, since their introduction as a tool, the use of social network approaches has changed considerably alongside the questions to which they have been applied (Cantor et al., 2021;Croft et al., 2016;Pinter-Wollman et al., 2014). Increasingly, researchers have investigated dynamic networks which consider changes in social relationships over time (Farine, 2018; or multilayer networks which consider different types of interaction or association within the same network object (Finn et al., 2019;Silk, Finn, et al., 2018). More recently, there has been a push in the network science community to embrace network approaches that move beyond solely considering dyadic representations of interactions (Musciotto et al., 2022;Silk et al., 2022).
As a result, there are now diverse options available to an animal behaviour researcher when choosing a conceptual representation of their social system, even prior to selecting appropriate statistical analyses or modelling approaches. Here, instead of a detailed 'How To', I provide an overview of the principal conceptual representations of relational data sets in animal societies. I also draw attention to more detailed resources for less-used approaches and offer guidance on when different approaches are most valuable. Even for the same data set it is possible to represent interaction or association data in different ways, meaning decisions about the best approach to use should depend first and foremost on the research questions of interest (Carter et al., 2015) and second on any limitations inherent to the data set analysed. I hope to provide a resource that can be valuable for researchers designing animal social network projects and analyses (e.g. for preregistered studies or funding applications) as well as for those faced with previously collected data with particular limitations or constraints.

THE BUILDING BLOCKS OF NETWORKS FOR ANIMAL BEHAVIOUR
The basics of how to construct networks in ecology (Proulx et al., 2005) and animal social behaviour (e.g. Croft et al., 2008;Farine & Whitehead, 2015) have been discussed extensively elsewhere so I provide only a very brief overview that indicates the scope and focus of this paper.
Networks consist of nodes or vertices connected by links or edges between them. In most animal social networks, nodes will represent individuals. However, nodes can also represent particular groups, locations (e.g. burrows, watering holes, food resources) or time points to which individuals are connected. While not strictly social networks, movement networks in which nodes represent locations and edges the movements of individuals (Jacoby & Freeman, 2016) also provide valuable tools to study animal social behaviour. Edges represent some form of interaction or association between the nodes. Examples in animal social behaviour include specific behavioural interactions (e.g. grooming, aggressive interactions), close contact (e.g. as recorded using proximity loggers) or co-occurrence of individuals within a group or at a particular location. Sometimes edges will represent more abstract indications of the social relationship between individuals based on one or more of these data sources.
In typical network approaches all nodes will represent the same 'type' of entity (e.g. you would not mix individuals and locations) and edges only connect pairs of nodes (or dyads). However, alternative network representations also discussed below relax these restrictions. For example, bipartite networks can be used to represent networks with interactions only between two types of node (Larremore et al., 2014), multilayer networks allow the representation of different types of nodes and/or edges together, and higher-order network approaches allow for edges that connect more than two individuals. As a result, the full network toolkit available to researchers provides considerable flexibility to researchers that can be adapted to the questions they have.
An important note here is that, regardless of the network representation used, animal social network data are typically only a sample of the individuals (nodes), interactions or associations that occur (edges), or both the individuals and their interactions. Therefore, it is important to account for this appropriately with subsequent analyses and doing so will be especially important when sampling is biased or uneven. How best to do this will vary considerably depending on the research questions being asked, the method of data collection and the conceptual representation being used and is beyond the scope of this paper. However, readers are encouraged to explore the recent literature discussing statistical methodologies to deal with these sampling issues in a range of contexts Hart et al., 2021;Ross et al., 2022;Young et al., 2020).

Binary Networks
A binary, undirected network is the most basic representation of social relationships. Edges (or links) connect vertices (nodes) when two individuals share a meaningful social relationship. When measuring animal social networks these edges typically represent individuals detected in close proximity (e.g. contact networks: White et al., 2017), recorded in an aggregation or group together (Franks et al., 2010) or interacting in a specific way (e.g. grooming: Cowl et al., 2020;fighting: Hobson, Mønster, & DeDeo, 2021). A long history of researchers using binary, undirected networks means that there are a wealth of approaches available to study the position of individuals within the network, features intermediate between individual and group or population properties (mesoscale structure) such as cliques and communities, as well as properties of the network as a whole (see overviews provided by Croft et al., 2008;Wey et al., 2008;Farine & Whitehead, 2015;Silk, Croft, Delahay, Hodgson, Boots, et al., 2017). In addition, some measures calculated in more complex representations are inherently binary, such as degree (the number of connections an individual has). However, by representing social relationships as dyadic, unweighted and undirected (or by using binary measures) a considerable amount of information is typically lost meaning the use of unweighted networks in animal behaviour research is frequently cautioned against (see discussion and simulation studies in Franks et al., 2010;Croft et al., 2011;Farine, 2014;Farine & Whitehead, 2015), although can be useful occasionally as long as the edge weight threshold used is carefully justified (Croft et al., 2011). In R, representation and basic analysis of binary networks is possible using the packages igraph (Csardi & Nepusz, 2006), sna (Butts, 2008a(Butts, , 2023 and network (Butts, 2008b(Butts, , 2015 among others.

Weighted Networks and Multigraphs
One easy way to add information to a network representation is to incorporate data on the frequency, duration or strength of social relationships. In weighted networks (Fig. 1a), edges are assigned a value to indicate the strength of the connection between two individuals. Relatively early in the history of animal social network analysis, the importance of using weighted edges to represent interactions and associations was recognized (Farine, 2014;Franks et al., 2010), and a wide variety of different ways of weighting edges are now available for researchers to use in different contexts, such as commonly used association indices (Hoppitt & Farine, 2018) or equivalents that retain information on the number of observations (Hart et al., 2021). Most common network analyses have now been generalized for weighted networks including many (a) (c) (b) Figure 1. Examples of (a) a weighted network in which edge width represents the total duration of interactions, (b) an unweighted multigraph in which the number of edges in a dyad represents the number of interactions between two individuals, and (c) a weighted multigraph in which the number of edges in a dyad represents the number of interactions between two individuals and the width of each edge illustrates the duration of each interaction. The weighted multigraph retains the most information about social interactions within the group. key network measures and community detection algorithms, typically using the same software packages highlighted in the previous section. In addition, a number of statistical tools have recently been developed that deal with sampling issues in weighted network representations that offer potentially powerful tools in animal social network analysis (see approaches described in Young et al., 2020;Hart et al., 2021;Ross et al., 2022). However, it can be very important to consider how edge weights are included in these calculations and subsequent analyses. For example, when calculating the shortest paths through the network (and measures derived from this such as betweenness and closeness centrality) edges with higher weights could be considered 'shorter' or 'longer' depending on context. Moreover, how the path length calculated depends on edge weight need not always have the same mathematical form. A key example of this is that default behaviour of the R package igraph (Csardi & Nepusz, 2006) treats edge weights as a cost (e.g. as if they are a distance) for some calculations (e.g. betweenness centrality, closeness centrality) while in many applications in animal behaviour the opposite is true, meaning the edge weights used have to be redefined when these calculations are used in behavioural ecology.
What is often neglected in animal social network research, however, is that repeated interactions can also be represented as a multigraph, where there is no constraint on the number of edges connecting a dyad (Fig. 1b). In some contexts, this might be a more appropriate way of representing the frequency of interactions between pairs of individuals (e.g. A groomed B 10 times), and it certainly helps to generate reference models for subsequent analysis more intuitively as edge rewiring algorithms (a permutation approach in which at each step the identity of nodes connected by a selected edge are changed) can be applied to each edge independently (Hobson, Silk, et al., 2021). In addition, for some animal network data sets including both the frequency and duration or strength of interactions could provide valuable additional information. In this case it is necessary to analyse a weighted multigraph (Fig. 1c). For example, when testing hypotheses in grooming networks it may be that the length of individual grooming bouts and frequency of grooming bouts provide independent information about the social relationship between two individuals. Taking this approach can open up new research questions about the relative importance of frequent versus long duration social interactions in group social structure and stability. It may also be important, for example, when studying social contagions if the likelihood of transmission depends on the duration of interactions (e.g. for less infective pathogens or for social learning of more complex behaviours). When using multigraphs in this way it will be important to control for variation in sampling effort (e.g. the number of times individuals were observed) if this varies among individuals when conducting subsequent statistical analyses. Using multigraphs can also create challenges when representing networks visually (especially with many edges between nodes) and is potentially more computationally intensive than using weighted networks. Therefore, using them should be reserved for contexts in which maintaining the independence of the frequency and duration of interactions provides valuable additional information on social relationships and their ecological and evolutionary consequences as outlined above. The R package igraph (Csardi & Nepusz, 2006) facilitates storing and representing weighted multigraphs.

Directed Networks
Another simple way to include additional information is to use a directed network. In directed networks (or digraphs) edges no longer simply represent a connection between node A and node B; they indicate a connection from node A to node B. Directed networks have proven especially useful for representing behavioural interactions, in which who initiates an interaction is important. For example, directed networks have been commonly used to provide insights into the structure of dominance hierarchies (Dey & Quinn, 2014;Hobson, Mønster, & DeDeo, 2021). When studying hierarchies, considering directed edges makes it possible to distinguish between transitive (individual I is dominant over individuals J and K, individual J is dominant over individual K) and cyclical (individual I is dominant over individual K, individual J is dominant over individual K and individual K is dominant over individual I) triads (Shizuka & McDonald, 2012;Dey & Quinn, 2014) or investigate reciprocity effects (Dey & Quinn, 2014; which are important indicators of the linearity and stability of dominance hierarchies. Directed edges have also proved valuable in studying grooming behaviour and affiliative interactions within groups (Balasubramaniam et al., 2018;Cowl et al., 2020). Finally, they have also provided valuable tools in studying movement behaviour, especially when it is possible to define discrete patches or locations that individuals move between (reviewed by Jacoby & Freeman, 2016). Many common measures and tools have been extended to use in directed networks, and some additional measures are available (e.g. PageRank centrality; Ding et al., 2009). Directed networks can be represented and relevant measures calculated using the same software tools as binary and weighted networks. Similarly, Bayesian statistical models that are designed to account for sampling issues common in empirical social network data can be applied to directed network data (see modelling frameworks provided by Hart et al., 2021;Ross et al., 2022).

Signed Networks
While conventionally nonzero edges or links have positive values (as for all the forms of network discussed so far), researchers in other fields have started to use signed networks (Beigi et al., 2016;Kirkley et al., 2019). In signed networks, positive (e.g. affiliative) interactions are assigned positive edge weights and negative (e.g. agonistic, avoidance) interactions are assigned negative edge weights (although in practice most analysis of signed networks has focused on binary versions in which edge weights are either þ1 or À1). Various applications of networks to study behavioural interactions in animal groups could lend themselves to the analysis of signed networks when there is information available about different types of interaction and these are considered to be either 'positive' or 'negative'. Perhaps the most direct application will be in comparing patterns of affiliative interactions (positive) with patterns of social avoidance (negative), especially given that social avoidance is relatively understudied in nonhuman animals (Strickland et al., 2017). Another context in which signed networks may be valuable is in comparing networks of affiliative and agonistic interactions, although note that for some research questions it may be more effective to integrate these behaviours as a multilayer network (see below).
Signed network approaches are likely to be especially beneficial when studying questions related to group stability (e.g. Larson et al., 2018;McCowan et al., 2011) and alliance formation (e.g. Connor et al., 2022). Structural balance theory (Ilany et al., 2013), which predicts, for example, that if two individuals share a strong mutual connection with a third individual they are unlikely to possess a negative social relationship, extends neatly into signed networks (see Fig. 1 in Facchetti et al., 2011). The presence of unbalanced triads (e.g. the triad described in the previous sentence) in a signed network could be used to predict network dynamics or changes in group composition. There may be interest in investigating the relative importance of structural imbalances involving different combinations of positive and negative ties. Similarly, the commonly used stochastic block model has been extended to signed networks with the aim of identifying clusters or communities characterized by positive interactions with each other but negative ties with other clusters (Jiang, 2015). This offers a very natural way to characterize complex social structures such as those dominated by matrilines or where alliances govern access to mates or reproductive opportunities. Analysis of signed networks in R can be conducted using the R package signnet (Schoch, 2020), an extension of igraph for signed networks.

Bipartite (Two-Mode) Networks
Bipartite (or two-mode) networks connect two different types of node with connections between the same type of node not possible (Larremore et al., 2014). They have been commonly used to study ecological networks such as plant e pollinator (Dupont et al., 2014;Miele et al., 2020) or host e pathogen (Valverde et al., 2020;Albery et al., 2021) networks. However, one of the classic social network data sets, the Davis' Southern women network, illustrates the potential values of bipartite networks in behavioural ecology. The Southern women network links a set of 18 women to the parties or events that they attended (Davis et al., 1941;Opsahl, 2013). This is equivalent to group-based methods of animal social network construction (Farine & Whitehead, 2015;Franks et al., 2010). These data sets can be naturally represented as a bipartite network linking individuals to particular groups or aggregations (see Case Study: Alternative network representations of animal groups). Frequently, this network is then collapsed into a weighted network using the gambit of the group assumption (see Case Study: Alternative network representations of animal groups). Other data sets such as mating networks (Fisher et al., 2016;McDonald & Pizzari, 2016) or those connecting individuals to locations they have visited (e.g. refuges, watering holes, foraging locations) are also a natural fit to bipartite representations (e.g. Sah et al., 2016). By representing these networks as bipartite rather than collapsing them to be conventional (unipartite) social networks, key structural information is maintained that would otherwise be lost. This can be very helpful in addressing particular questions. For example, in the case of group-based networks, these would include questions related to choices of group membership for individuals or in breaking down gregariousness into a tendency to be in more and/or larger groups. A wealth of tools is available to analyse bipartite networks, although predominantly tailored to other fields. For example, as well as (generalized) linear model approaches, exponential random graph models have been extended to incorporate bipartite dependency assumptions (Wang et al., 2013) and the R package bipartite (Dormann et al., 2008) provides the capability to calculate a range of measures and fit some more specialist models (albeit with the analysis of ecological rather than social networks in mind). Note that issues with biased sampling (and potentially also identification errors) that apply to dyadic network representations will also apply to the statistical analysis of bipartite networks, requiring careful consideration during statistical model design. For example, (1) when constructing bipartite mating networks individuals are likely to be better connected if observed more frequently unless this is taken into account, or (2) when using bipartite networks to link individuals to particular spatial locations individuals that frequent the centre of a study area and so visit monitored locations more frequently will typically appear better connected unless this is controlled for adequately in the analysis.

Tripartite Networks
It is also possible to represent animal behaviour with additional layers of complexity. For example, Manlove et al. (2018) demonstrated how it is possible to use a tripartite network as a conceptual tool to integrate movement and social behaviour. These networks contain three types of node: individuals, spatial locations and time points. Individuals and locations are linked via nodes representing time points. It is then possible to collapse this network into various bipartite and unipartite networks commonly used in behavioural ecology research (see Fig. 2 in Manlove et al., 2018).

Multilayer Networks
Multilayer networks provide a general framework to represent dyadic networks between different types of entity and/or containing different types of social relationships (Kivel€ a et al., 2014). They contain different network layers, with edges possible both within (intralayer edges) and between (interlayer edges) them. Because animal populations and groups frequently contain social networks nested within a wider spatial network (Silk, Finn, et al., 2018;Webber et al., 2023), and multiple types of social interaction network can interact with one another within animal groups (Barrett et al., 2012;Beisner et al., 2015), multilayer networks have great potential as a tool in animal behaviour research (Finn et al., 2019).
There are two broad categories of multilayer network. Multiplex networks (typically) contain different sets of interactions between the same set of actors (Kivel€ a et al., 2014). For example, they could be applied in scenarios where a researcher was studying networks of agonistic behaviour, ritualized dominance interactions and submissive behaviours among the same set of individuals . Interconnected networks are most commonly used to represent systems in which layers contain different types of node. This could be different phenotypes (Silk, Weber, et al., 2018) but could also represent different species or combinations of species and spatial locations. For example, Silk, Drewe, et al. (2018) used an interconnected network to represent contact networks between wild European badgers, Meles meles, domestic cattle, Bos taurus, and badger latrine locations. This enabled identification of likely inter-and intraspecific transmission pathways for Mycobacterium bovis, the causative agent of bovine tuberculosis.
The use of multilayer approaches has expanded greatly in recent years and there is now a wealth of tools available to analyse them, especially for multiplex networks. These are well summarized by Finn et al. (2019) and Finn (2021). The package muxViz provides a user-friendly interface for basic multilayer network analysis in R (De Domenico et al., 2015), with additional R packages tailored to multiplex network analysis including multinet (Magnani et al., 2021) and multiplex (Ostoic, 2020).

Higher-Order Network Approaches
All the approaches discussed so far assume that interactions or associations are dyadic, that is, that they occur between pairs of individuals. However, this is clearly a simplification for many common types of social data (Musciotto et al., 2022). In some cases, explicitly incorporating higher-order interactions (i.e. those simultaneously occurring between more than two individuals) can change our understanding of the emergent properties of a system, for example the spread of pathogens or behaviours (Iacopini et al., 2019(Iacopini et al., , 2022Noonan & Lambiotte, 2021). Despite this, explicit higher-order representations of nonhuman animal social networks have been used only very rarely.
There are three commonly used ways to represent higher-order interactions in network science: hypergraphs, simplicial sets and simplicial complexes (Silk et al., 2022). Hypergraphs are a generalization of dyadic networks that enable (hyper)edges to connect any number of individuals (Battiston et al., 2020;Torres et al., 2021). For example, three individuals A, B and C observed together in a single group could all be connected with a single hyperedge (or hyperlink). Hypergraph representations of grouping-event-based networks is discussed further in the section Case Study: Alternative network representations of animal groups.
Simplicial sets represent an alternative mathematical representation of these interactions using set notation (Silk et al., 2022). Each simplex in a simplicial set represents either a node/individual (0-simplex), dyadic interaction (1-simplex) or higher-order interaction (2-simplex, 3-simplex, etc.). However, unlike hypergraphs simplicial sets avoid the subedge problem (Silk et al., 2022); it is possible to represent relationships between individuals in the absence of individuals themselves without the introduction of any new notation in simplicial set but not hypergraph representations. For example, imagine a scenario where the presence or outcome of a dominance interaction between individual A and individual D is influenced by an alliance between individuals A, B and C. In this case the 2-simplex (A,B,C) influences the 1-simplex (A,D) even in the absence of B and C. A hypergraph representation cannot natively capture this component of social structure (Fig. 2).
A simplicial complex is a specific form of simplicial set which must contain all nested lower-order simplices. For example, if a simplicial complex contained the 2-simplex (I,J,K) it must necessarily also contain the 1-simplices (I,J), (I,K), (J,K), and 0-simplices (I), (J) and (K). In a social context this represents an assumption that any larger interaction or group inevitably includes all possible subgroups or interactions. While there are cases where this assumption will be met by real-world social behaviour, there are also many cases where not all subsets of individuals within a group can or will have interacted. Therefore, while mathematically convenient, simplicial complexes are likely to be less useful to animal behaviour research than either hypergraphs or simplicial sets.
The power of using higher-order approaches in modelling pathogen spread (Bod o et al., 2016;Iacopini et al., 2019) and behavioural contagions (Noonan & Lambiotte, 2021) has been clearly demonstrated by theoretical work. In behavioural disease ecology higher-order approaches may be particularly useful when there are nonlinear dose -response curves (Silk et al., 2022;St-Onge et al., 2021) and when there is considerable variation in group or aggregation size. For behavioural contagions, higher-order approaches can simplify the representation and modelling of complex contagions (Silk et al., 2022). This will be especially powerful when the presence of multiple demonstrators or receivers impacts social learning. However, descriptive measures of higher-order networks will also offer an information-rich approach to classifying animal social networks that can extend insights beyond dyadic networks, particularly when studying networks based on co-occurrence in a group (see Case Study: Alternative network representations of animal groups). Incorporating hypergraph or simplicial set approaches may even shape how we consider the role of the social environment in indirect genetic effects (Fisher & McAdam, 2017;Montiglio et al., 2018) if fitness is influenced by higher-order interactions.
Widely accessible implementations of higher-order network approaches are still in their infancy, but good overviews are provided by Battiston et al. (2020) and Torres et al. (2021) and a guide to available software for visualization and basic analyses in R, Python and Julia is available in Silk et al. (2022).

CASE STUDY: ALTERNATIVE NETWORK REPRESENTATIONS OF ANIMAL GROUPS
There is frequently no one single way to represent interactions as a social network. A good example is in considering possible network representations of animal social groups (Fig. 3). Traditionally in animal social network analysis researchers have used the gambit of the group assumption (Franks et al., 2010) that any pair (dyad) of individuals in a group have associated and therefore share a connection in a weighted social network. The weight of their connection is often calculated as a function of the proportion of times they are observed together (with a variety of potential functions available; Hoppitt & Farine, 2018). However, this representation is a simplification of a more complex network structure which can be captured as either: (1) a bipartite network in which one set of nodes represents individuals and another set of nodes observed grouping events or aggregations with edges connecting individuals to the aggregations in which they occurred; or (2) a [weighted] hypergraph (or simplicial set) in which a hyperedge connects all of the individuals that occurred in each group.
Here we provide a case study (Supplementary Materials) in which three research teams study the same social system. Because they are asking different questions using the data set they elect to use different network approaches to represent it. Research Team 1 are interested in whether individual social relationships are assorted by different phenotypic traits. Because the goal of their study is to infer potential social relationships in the population (with the assumption that individuals with strong social relationships will be found together more often in groups) using a dyadic network representation distils relevant information conveniently and provides an effective way to answer their question.
However, in other contexts the weighted (dyadic) network represents a simplification that loses some information about the system. Research Team 2 are more interested in properties of the social groups themselves, specifically whether the social centrality (degree and strength) of individuals is better explained by the size of groups they occur in or the number of times they are in groups (i.e. not observed by themselves) and whether smaller groups tend to consist of subsets of larger groups (i.e. are they nested?). For questions such as these that are more related to the social decision making of individuals, bipartite network and hypergraph representations are likely to be more suitable as they retain information about group size and composition. In this case, directly modelling the bipartite network could offer real potential, being sufficient to answer their first question and providing ideal tools (nestedness calculations from the ecological networks literature) to answer the second.
The power of higher-order (e.g. hypergraph) approaches becomes valuable if the nondyadic nature of interactions is likely to be important in some way, especially in studies of contagions (e.g. pathogens, information, behaviours), for example. Our third team are disease ecologists who are interested in the potential spread of an emergent pathogen through the population. Because of how it is transmitted they feel that the nondyadic nature of social interactions in the system may contribute to its spread, and they compare hypergraph and dyadic network outbreak models to assess its potential impact. For the set of parameters they consider, the importance of considering the nondyadic nature of interactions is very evident (although if you change these parameters, you will see how this changes according to the size of infectious dose and how infectious dose affects the transmission probability of the pathogen). Similarly, nondyadic interactions may also change the dynamics of other social contagions such as the spread of behaviour (Iacopini et al., 2019(Iacopini et al., , 2022. Collectively, these examples illustrate the advantages of illustrating the same network data in different ways, in particular highlighting how it pays to start with the research question or hypothesis of interest, determine which features of the data are of most importance (and need to be maintained), and then select an appropriate method of representing the network. One thing to note is that the differences between representations can sometimes be conceptual more than practical, for example the group-byindividual matrix used to represent the bipartite network is equivalent to the incidence matrix for a hypergraph representation. Also note that it is possible to answer the same question using different representations, for example phenotypic assortativity is apparent in the bipartite network (and analogously the hypergraph) representations as well as the dyadic one. Finally, it is also likely that for some studies combining information from multiple representations will be beneficial to addressing research goals. I have illustrated the example of group-based networks as it is conceptually intuitive, but a similar process is important to follow for other forms of data as well (e.g. association networks based on shared resource use, association networks based on cocapture data).

DYNAMIC NETWORKS
So far all of the network representations have been discussed in a static context, i.e. not considering the fact that interactions or relationships may change over time. However, most network data are dynamic, and it can often be helpful to consider how social network structure and the position of individuals within it changes over time (Farine, 2018;Pinter-Wollman et al., 2014). For example, when considering pathogen transmission or the spread of information and behaviours, the frequency with which interaction patterns change can be just as important as social structure in determining the outcome (Evans et al., 2020). There are two major ways to consider dynamic network data, as aggregated or snapshot static networks or as time-ordered networks (Blonder et al., 2012;Fig. 4).
The former represents a convenient approach as it facilitates the application of the same (or broadly similar) analytical tools as for static networks. Snapshot networks are a series of networks representing associations or interactions occurring at a series of specific points in time (e.g. the 1 m proximity networks arising from successive scan samples of a group conducted every hour). For time-aggregated networks there is flexibility in the time periods over which interactions or associations are collated. Often the time periods used are discrete from each other (e.g. daily networks, seasonal networks); however, it is also possible to generate timeaggregated networks based on overlapping windows (e.g. 3monthly networks that run from January to March, February to April, March to May, etc.).
Basic descriptive network measures (whether at the network or individual level) can characterize the stability of overall social structure (Pinter-Wollman et al., 2014) and the consistency with which individuals occupy positions within it (Wilson et al., 2013). Because time-aggregated networks can also be considered as multiplex networks (with different layers representing different time periods), descriptive measures designed for multilayer networks may also have value for some research questions (Finn et al., 2019). Similarly, various statistical models have been designed that specifically analyse these time-aggregated (or snapshot) networks. For example, network autocorrelation models (Silk, Croft, Delahay, Hodgson, Weber, et al., 2017), exponential random graph models (Lusher et al., 2012) and stochastic block models (Matias & Miele, 2017) have all been extended to time-aggregated networks. They can be used to answer questions (a) (b) (c) Figure 3. Representations of the same set of animal groups as (a) a bipartite network connecting individuals (black circles) to the grouping events (grey squares) in which they were recorded; (b) a hypergraph connecting individuals (black circles) with hyperedges according to the groups in which they were observed; and c) a weighted network in which the weight of dyadic connections represents the number of groups in which two individuals were observed together. Each of these approaches retains different levels of information about the social associations that occurred and lends itself naturally to different analytic approaches and research questions.
about individual traits, interactions/relationships and network community structure respectively, incorporating temporal variability and time-lagged variables. Further models designed specifically for time-aggregated networks are also available, for example stochastic actor-oriented models (Snijders et al., 2010;. It is also possible to apply these statistical models in other ways, for example the epimodel R package (Jenness et al., 2018) employs temporal exponential random graph models to facilitate simulations of network epidemiological models. When applying more complex statistical models to timeaggregated networks generated from overlapping time windows (i.e. using subsets of observations that are not fully independent from each other) it is important to ensure this does not violate assumptions of the model being used.
However, while time-aggregated networks are appropriate for answering a wide range of questions in behavioural ecology, they represent a simplification of the true social dynamics. Consequently, for some applications where the specific order of interaction sequences is important it is necessary to use time-ordered networks. Commonly encountered examples in behavioural ecology are in directed behavioural interactions within groups such as grooming and dominance interactions. For example, Elo ratings, now often used to study dominance hierarchies in animal groups (Neumann et al., 2011;Neumann & Fischer, 2023;S anchez-T ojar et al., 2018), can exploit the information provided by the order in which interactions occur. Using time-ordered networks might also be important when answering fine-scale questions about social contagions in networks. For example, retaining time-ordered interactions is important when quantifying social transmission (Gilbertson et al., 2018;Silk, Croft, Delahay, Hodgson, Boots, et al., 2017). Although tools to analyse time-ordered networks are scarcer than for time-aggregated networks, various approaches are available. Measures such as burstiness (Stehl e et al., 2010) can quantify the temporal distribution of interactions, which can be important in explaining complex social contagions (Evans et al., 2020), for example. Statistical models include relational event models for directed, time-order networks (Patison et al., 2015;Tranmer et al., 2015) and dynamic network actor models (Stadtfeld et al., 2017) for undirected relationships. The latter could be applied very naturally to study the dynamics of alliances within animal groups and can be implemented in R using the package goldfish (Hollway & Stadtfeld, 2022).

EGO NETWORKS
Ego networks represent only individuals (nodes) with which a single focal individual associates, interacts or shares a social relationship, along with the social connections between these neighbours (Fig. 5). If desired, ego networks can be weighted, signed, multiplex, dynamic, etc., in the same way as population or group level networks (Liu et al., 2018;Rezaeipanah et al., 2020;Wang et al., 2020). The package egor (Krenz et al., 2022) provides tools for ego network representation, visualization and analysis in R. While ego networks are commonly used in sociological research, this has not extended to animal behaviour. Ego network analyses and measures typically focus on how embedded an individual is  (a) (b) Figure 5. An illustration of a focal individual (red node) within (a) its group level network and (b) its ego network. Ego network analysis can be used to focus on the immediate social neighbourhood of individuals or when it is prohibitive to sample the entire network. within its network neighbourhood or the extent to which it acts as a bridge between different neighbourhoods (Butts, 2008c). While many of these questions can be addressed using measures of individual social network position in group or population level networks, ego networks are well suited to contexts where there are constraints on sampling intensity or wider population data are very sparse. The ego network approach is also well suited to social network studies that use a focal follow approach (where networks are constructed based on successively following different individuals and recording their social associations and/or interaction partners) as, in these cases, the full network is constructed from separate ego networks from each focal follow anyway. As a result, while their applications in behavioural ecology will likely be more limited, ego networks are an approach to bear in mind when addressing questions about the social role of particular subsets of individuals especially if there are limitations that require lower levels of sampling. For example, assessing the consistency of an individual's social environment can easily be assessed by calculating the stability of its ego network. Similarly, the redundancy of an ego within its ego network provides a good alternative measure of how embedded an individual is within its network. Both these aspects of the social environment have the potential to influence fitness-related traits.

GENERAL RECOMMENDATIONS FOR CHOOSING BETWEEN APPROACHES
With such diverse approaches available and many applicable to the same data sets, choosing the best representation is not always easy. However, there are a few general rules that can help. (1) The research question should always be central to driving the choice of network analyses applied, and this extends beyond how edges are defined (Carter et al., 2015;Farine & Whitehead, 2015) to broader considerations around network representations. For example, higher-order networks provide valuable additional information when researchers are interested in the ecological or evolutionary effects of larger (nondyadic) interactions, that is, nondyadic effects.
(2) Sampling constraints are important when selecting representations to use. More complex approaches such as multilayer and dynamic network analyses are more data hungry and require more time-intensive sampling. Ego network analyses can be helpful in situations with patchily distributed sampling effort. (3) Collecting 'too much' data will only be an issue when making decisions about where to target resources (e.g. ego networks of individuals in 20 social groups versus a full network of two social groups). In other contexts, recording data in a way that may allow more complex representations to be used (e.g. recording frequency and duration of interactions, recording timings of interactions, etc.) will likely be worthwhile even if simpler network representations will probably be used in the long run. (4) Some newer approaches have less welldeveloped or widely accessible analytical tools (e.g. signed and higher-order networks) which may limit the analyses possible without developing functions or algorithms for yourself (5) Some approaches (e.g. weighted multigraphs, higher-order approaches). will be more computationally intensive than others, and should therefore only be used when they offer a clear advantage for answering a specific research question if computational resources are to be used responsibly.

CONCLUSIONS
Network analysis has a huge amount to offer behavioural ecology but frequently represents a major challenge to those encountering it for the first time. Fortunately, there are some valuable introductory papers to offer guidance on data collection, descriptive statistics and statistical modelling in networks (e.g. Butts, 2008c;Cranmer et al., 2017;Farine, 2017;Farine & Whitehead, 2015;Hart et al., 2021;Hobson, Silk, et al., 2021;Pinter-Wollman et al., 2014;Silk, Croft, Delahay, Hodgson, Weber, et al., 2017). This overview complements that existing guidance by highlighting the diversity of the applied network analysis toolkit now available and drawing attention to the different ways to think about and represent animal social networks. It reveals the power of considering alternative options to quantify networks in animal behaviour research, and the potential value of newer approaches to answer key research questions related to social and spatial behaviour.

Author Contributions
Matthew Silk: Conceptualization; Funding acquisition; Project administration; Visualization; Writing e original draft; Writing e review & editing.

Declaration of Interest
None.