A fast and complete algorithm for enumerating pseudo-cliques in large graphs

This paper discusses a complete and efficient algorithm for enumerating densely connected $$k$$k-Plexes in networks. A $$k$$k-Plex is a kind of pseudo-clique which imposes a disconnection upper bound (DUB) involving a parameter k for each constituent vertex. However, because the parameter value is usually set independently of the sizes of the targeted pseudo-cliques, we often obtain $$k$$k-Plexes that are not densely connected. To overcome this drawback, we introduce another constraint, the connection lower bound (CLB), which involves a parameter j. Using the CLB, we can enjoy monotonic j-core operations and can design an efficient depth-first algorithm, which can exclude both search branches that generate duplicate search nodes and “hopeless” nodes that yield no targets satisfying both DUB and CLB. Our experimental results show that the algorithm can be a useful tool for detecting densely connected pseudo-cliques in large networks, including an example with over 800, 000 vertices.

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