Data Mining and Knowledge Discovery

, Volume 30, Issue 5, pp 1134–1165 | Cite as

Top-k overlapping densest subgraphs

  • Esther Galbrun
  • Aristides Gionis
  • Nikolaj TattiEmail author


Finding dense subgraphs is an important problem in graph mining and has many practical applications. At the same time, while large real-world networks are known to have many communities that are not well-separated, the majority of the existing work focuses on the problem of finding a single densest subgraph. Hence, it is natural to consider the question of finding the top-k densest subgraphs. One major challenge in addressing this question is how to handle overlaps: eliminating overlaps completely is one option, but this may lead to extracting subgraphs not as dense as it would be possible by allowing a limited amount of overlap. Furthermore, overlaps are desirable as in most real-world graphs there are vertices that belong to more than one community, and thus, to more than one densest subgraph. In this paper we study the problem of finding top-k overlapping densest subgraphs, and we present a new approach that improves over the existing techniques, both in theory and practice. First, we reformulate the problem definition in a way that we are able to obtain an algorithm with constant-factor approximation guarantee. Our approach relies on using techniques for solving the max-sum diversification problem, which however, we need to extend in order to make them applicable to our setting. Second, we evaluate our algorithm on a collection of benchmark datasets and show that it convincingly outperforms the previous methods, both in terms of quality and efficiency.


Community detection Overlapping communities Social network analysis Dense subgraphs Diverse subgraphs Approximation algorithm 


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Esther Galbrun
    • 1
  • Aristides Gionis
    • 2
  • Nikolaj Tatti
    • 2
    Email author
  1. 1.Inria Nancy – Grand EstVillers-lès-NancyFrance
  2. 2.Helsinki Institute for Information Technology (HIIT) and Department of Computer ScienceAalto UniversityHelsinkiFinland

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