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Discovering Hierarchical Subgraphs of K-Core-Truss

  • Zhen-jun Li
  • Wei-Peng Zhang
  • Rong-Hua LiEmail author
  • Jun Guo
  • Xin Huang
  • Rui Mao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10569)

Abstract

Discovering dense subgraphs in a graph is a fundamental graph mining task, which has a wide range of applications in social networks, biology and graph visualization to name a few. Even the problems of computing most dense subgraphs (e.g., clique, quasi-clique, k-densest subgraph) are NP-hard, there exists polynomial time algorithms for computing k-core and k-truss. In this paper, we propose a novel dense subgraph, \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\), that leverages on a new type of important edges based on the concepts of k-core and k-truss. Compared with k-core and k-truss, \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) can significantly discover the interesting and important structural information outside the scope of the k-core and k-truss. We study two useful problems of \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) decomposition and \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) search. In particular, we develop a \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) decomposition algorithm to find all \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) in a graph G by iteratively removing edges with the smallest \(\mathsf {degree}\)-\(\mathsf {support}\). In addition, we propose a \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) search algorithm to identify a particular \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) containing a given query node such that the core-number k is the largest. Extensive experiments on several web-scale real-world datasets show the effectiveness and efficiency of the \(\mathsf {k}\)-\(\mathsf {core}\)-\(\mathsf {truss}\) model and proposed algorithms.

Notes

Acknowledgement

We thank anonymous reviewers for their insightful comments. The work was supported in part by NSFC Grants (61402292, U1301252, 61033009), NSF-Shenzhen Grants (JCYJ20150324140036826, JCYJ20140418095735561), and Startup Grant of Shenzhen Kongque Program (827/000065).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Zhen-jun Li
    • 1
  • Wei-Peng Zhang
    • 1
  • Rong-Hua Li
    • 1
    Email author
  • Jun Guo
    • 1
  • Xin Huang
    • 2
  • Rui Mao
    • 1
  1. 1.College of Computer Science and Software EngineeringShenzhen UniversityShenzhenChina
  2. 2.Hong Kong Baptist UniversityHong KongChina

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