Determining groups from the clique structure in large social networks

Abstract Ethnographers have traditionally defined human groups as disjoint collections of individuals who are linked to each other by regular interaction, shared perceptions and affective ties. They are internally differentiated: some members occupy a central position in the group, others are on the periphery or somewhere in between. This way of characterising a group is intuitive to seasoned observers but social network analysts seek a more systematic method for determining groups. Freeman [Freeman, L.C., 1996. Cliques, Galois lattices, and the structure of human social groups, Social Networks 18, 173–187.] describes a formal model based on the concept of overlapping social network cliques. Freeman's analysis produces results that are consistent with ethnographic results but his technique is not easily implemented for very large data sets. This paper describes two algorithms based on Freeman's clique–lattice analysis. The first implements his technique exactly; the second is a modification that exploits the clique structure, thereby enabling the analysis of large complex networks. We apply both algorithms to a real data set and compare the results.