Table 1.

Social network-based measures of indirect connectedness most commonly used in animal behaviour research

Indirect measure	Definition
Betweenness	The total number of shortest paths (routes of connections that can be followed on a graph from one actor to another) that pass through an individual linking other members of the social group to each other. Individuals with high betweenness tend to connect what would otherwise be unconnected parts of a network. High betweenness also represents individuals that have a large influence on the transfer of items through a network, based on the assumption that items follow the shortest paths (Freeman, 1977). These ‘items’ can include anything from information and disease, to cultural practices and money. As such, individuals with high betweenness are typically characterized as the ‘brokers’ of a network (Newman, 2003; Wasserman and Faust, 1994).
Clustering coefficient	Represents the nature of an individual’s local social network by measuring the proportion of an individual’s social partners who are partners with each other (Newman, 2003). Clustering coefficient is therefore a local measure of cliquishness or subgrouping. Clustering coefficient values range from zero to one, with zero indicating that none of an individual’s social partners are partners with each other, and one indicating that all of an individual’s social partners are also partners with one another.
Eigenvector centrality	A measure of both the number and quality of a subject’s social partners. Individuals with high eigenvector centrality have a large number of partners, who themselves have a large number of partners (Wasserman and Faust, 1994). This is based on the concept that connections to highly connected individuals contribute more to the score of the individual in question than do connections to poorly connected individuals, which is important in a variety of nonbiological contexts, such as the algorithm Google uses to rank webpages.
Reach	Represents the extent to which individuals are connected based on their degrees of separation from others. It is calculated by counting the number of nodes that each node can reach in k or less steps. For k = 1, reach is equivalent to degree centrality. Reach is perhaps most famously known from Stanley Milgram’s ‘six-degrees of separation’ study in which he demonstrated that a piece of mail was delivered to its specified recipient after passing through six individuals, only the latter of which was acquainted with the recipient (Milgram, 1967).
Farness centrality	The farness of an individual is defined as the sum of the shortest path lengths to all other nodes.
Closeness centrality	The inverse of farness centrality. Closeness can be interpreted to represent the amount of time it would take to spread an item (e.g. information) from one individual to all others (Sabidussi, 1966).
Information centrality	Evaluates how often an individual lies along a path between other individuals. Information centrality is similar to betweenness, but instead of following only the shortest paths, it also uses more circuitous paths (Newman, 2003; Stephenson and Zelen, 1989; Wasserman and Faust, 1994).