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 (.1,.2)-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 (.1,.2)-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 quasicliques, 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.