Finding Hierarchical and Overlapping Dense Subgraphs using Nucleus Decompositions
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique, kdensest subgraph) are NPhard. Furthermore, the goal is rarely to nd the \true optimum", but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine a hierarchical structure among them. Current dense subgraph nding algorithms usually optimize some objective, and only nd a few such subgraphs without providing any hierarchy. It is also not clear how to account for overlaps in dense substructures. We de ne the nucleus decomposition of a graph, which represents the graph as a forest of nuclei. Each nucleus is a subgraph where smaller cliques are present in many larger cliques. The forest of nuclei is a hierarchy by containment, where the edge density increases as we proceed towards leaf nuclei. Sibling nuclei can have limited intersections, which allows for discovery of overlapping dense subgraphs. With the right parameters, the nuclear decomposition generalizes the classic notions of kcores and ktrusses. We give provable e cient algorithms for nuclear decompositions, and empirically evaluate their behavior inmore »
 Authors:

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 The Ohio State Univ., Columbus, OH (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 OSTI Identifier:
 1172917
 Report Number(s):
 SAND201419934R
543218
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Technical Report
 Research Org:
 Sandia National Laboratories (SNLCA), Livermore, CA (United States)
 Sponsoring Org:
 USDOE; DARPA
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING kcore; ktruss; decomposition; hierarchy; overlapping subgraphs; dense subgraph discovery
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