Maximal Directed Quasi -Clique Mining

Quasi-cliques are a type of dense subgraphs that generalize the notion of cliques, important for applications such as community/module detection in various social and biological networks. However, the existing quasi-clique definition and algorithms are only applicable to undirected graphs. In this paper, we generalize the concept of quasi-cliques to directed graphs by proposing (γ1, γ2) -quasi-cliques which have density requirements in both inbound and outbound directions of each vertex in a quasi-clique subgraph. An efficient recursive algorithm is proposed to find maximal (γ1,γ2)-quasi-cliques which integrates many effective pruning rules that are validated by ablation studies. We also study the finding of top-k large quasi-cliques directly by bootstrapping the search from more compact quasi-cliques, to scale the mining to larger networks. The algorithms are parallelized with effective load balancing, and we demonstrate that they can scale up effectively with the number of CPU cores.