Detecting large cohesive subgroups with high clustering coefficients in social networks

•A new clique relaxation, α cluster, is introduced.•Structural properties of α clusters in social networks are investigated.•Optimization methods for finding large α clusters are proposed.•A clustering technique based on α clusters is developed.•Results of numerical experiments with social networks are reported.

Clique relaxations are used in classical models of cohesive subgroups in social network analysis. Clustering coefficient was introduced more recently as a structural feature characterizing small-world networks. Noting that cohesive subgroups tend to have high clustering coefficients, this paper introduces a new clique relaxation, α-cluster, defined by enforcing a lower bound α on the clustering coefficient in the corresponding induced subgraph. Two variations of the clustering coefficient are considered, namely, the local and global clustering coefficient. Certain structural properties of α-clusters are analyzed and mathematical optimization models for determining α-clusters of the largest size in a network are developed and validated using several real-life social networks. In addition, a network clustering algorithm based on local α-clusters is proposed and successfully tested.