Top-k overlapping densest subgraphs

Esther Galbrun 1 Aristides Gionis 2, 3 Nikolaj Tatti 3, 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : 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-kdensest 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-koverlapping 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.
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Esther Galbrun, Aristides Gionis, Nikolaj Tatti. Top-k overlapping densest subgraphs. Data Mining and Knowledge Discovery, Springer, 2016, 30 (5), pp.1134 - 1165. ⟨10.1007/s10618-016-0464-z⟩. ⟨hal-01399184⟩

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