Social network analysis for social neuroscientists

Abstract

Although social neuroscience is concerned with understanding how the brain interacts with its social environment, prevailing research in the field has primarily considered the human brain in isolation, deprived of its rich social context. Emerging work in social neuroscience that leverages tools from network analysis has begun to advance knowledge of how the human brain influences and is influenced by the structures of its social environment. In this paper, we provide an overview of key theory and methods in network analysis (especially for social systems) as an introduction for social neuroscientists who are interested in relating individual cognition to the structures of an individual's social environments. We also highlight some exciting new work as examples of how to productively use these tools to investigate questions of relevance to social neuroscientists. We include tutorials to help with practical implementations of the concepts that we discuss. We conclude by highlighting a broad range of exciting research opportunities for social neuroscientists who are interested in using network analysis to study social systems.

Keywords: network analysis; social networks; social neuroscience.

Fig. 1

Approaches to study and mathematically represent social networks. (a–c) In a sociocentric approach, one characterizes relationships between all members of a bounded social network. (a) A graphical representation of an undirected, unweighted sociocentric network that represents friendships between members of a bounded community. The colored circles are nodes (also called vertices), which represent individuals in the social network. The lines between the nodes are edges, which encode friendships or some other relationship between individuals. (b) One can also represent networks with an edge list, which is a list of all direct connections between nodes. (c) It is also common to represent an n-node network with an adjacency matrix A of size n × n (with n = 10 in this example). The elements A_ij of A encode the edges (both their existence and their weights) between each node pair (i, j) in a network. In an undirected, unweighted network (such as the networks in this figure), an associated adjacency matrix is symmetric. For example, the edge between Nick and Jen yields a 1 in the associated element of an adjacency matrix. (d–f) In an egocentric approach, one characterizes relationships in a network from an ego’s point of view. Suppose that we obtain information about the same social network as the one in the left column from interviewing only Mike, a single member of the network. This gives us Mike’s ego network. We draw solid lines based on Mike’s responses about his direct friendships and dotted lines based on his responses about whether his friends are also friends with one another. Comparing the graph from the sociocentric and egocentric approaches illustrates that the latter is missing information about several of the edges between the nodes (e.g. those between Nick and Elena, Nick and Jen, and so on). We also see this in the ego network’s associated (e) edge list and (f) adjacency matrix.

Fig. 2

An illustration of Stanley Milgram’s small-world experiments that demonstrate social distance. In their pioneering studies of social distance, social psychologist Stanley Milgram and colleagues (1967,1969) concluded that, on average, people are separated by six or fewer social connections. As our illustration demonstrates, individuals in the Midwestern United States (the starting position) were able to send a package to a stranger in Massachusetts (the target individual) through a path with a length of about 6. In one experiment, of the 160 packages that started in Nebraska (the starting position in this figure), 44 packages successfully arrived at the target individual. These 44 packages traversed about 6 edges on average. Milgram’s small-world experiments illustrate unweighted social distance in a real-life context.

Fig. 3

A few common measures of centrality. We use an adapted version of Krackhardt’s kite graph (Krackhardt, 1990) to illustrate several variants of centrality. (a) An example friendship network, with each node labeled with the name of an individual. (b–d) Variations of the same network, with the nodes resized to reflect the value of a particular centrality measure. (b) Degree centrality (i.e. degree) is the number of other nodes to which a node is connected directly (i.e. adjacent). Mike has a degree of 7, the largest value in the network. (c) Eigenvector centrality captures how well-connected a node is to well-connected others. Although Elena, Dan, and Sam all have the same degree (it is 3), Sam has a much smaller eigenvector centrality, as his friendships are with relatively poorly connected individuals. (d) Betweenness centrality captures the extent to which a node lies on shortest paths between pairs of nodes. Sam has the largest betweenness centrality in this network, because he connects many nodes in the network that otherwise would be on disconnected components of the network.

Fig. 4

Examples of multilayer networks. (a) A multiplex network is a type of multilayer network in which each layer has a different type of edge and interlayer edges can occur only between corresponding nodes in different layers. The nodes in this example represent the same individuals in each layer, and the edges in different layers encode different types of social relationships. We do not show any interlayer edges. In the first layer, edges encode friendships between individuals, whereas edges encode professional relationships between individuals in the second layer and recreational relationships between individuals in the third layer. (b) In this more general example of a multilayer network, the first layer encodes the same friendship network that we showed in (a). The second layer is a restaurant network, where nodes represent restaurants and intralayer edges encode culinary collaborations between restaurants. Interlayer edges encode restaurant patronage of a restaurant by an individual, with an edge indicating that an individual has visited a restaurant. This type of multilayer network can help one understand possible relationships between friendship groups and restaurant-patronage patterns. In this example, friends tend to eat at the same restaurants.