Finding maximal homogeneous clique sets

A linear delay algorithm for enumerating all connected induced subgraphs

Background

Real biological and social data is increasingly being represented as graphs. Pattern-mining-based graph learning and analysis techniques report meaningful biological subnetworks that elucidate important interactions among entities. At the backbone of these algorithms is the enumeration of pattern space.

Results

We propose an efficient algorithm for enumerating all connected induced subgraphs of an undirected graph. Building on this enumeration approach, we propose an algorithm for mining all maximal cohesive subgraphs that integrates vertices’ attributes with subgraph enumeration. To efficiently mine all maximal cohesive subgraphs, we propose two pruning techniques that remove futile search nodes in the enumeration tree.

Conclusions

Experiments on synthetic and real graphs show the effectiveness of the proposed algorithm and the pruning techniques. On enumerating all connected induced subgraphs, our algorithm is several times faster than existing approaches. On dense graphs, the proposed approach is at least an order of magnitude faster than the best existing algorithm. Experiments on protein-protein interaction network with cancer gene dysregulation profile show that the reported cohesive subnetworks are biologically interesting.