2016
DOI: 10.1007/s10618-016-0464-z
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Top-k overlapping densest subgraphs

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-k densest subgraphs. One major challenge in addressing this question is how to handle overlaps: eliminating overlaps completely is one optio… Show more

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Cited by 58 publications
(60 citation statements)
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“…Exact algorithms [14], [15] and approximate algorithms [10], [15] have been proposed for finding subgraphs with maximum average degree. These have been extended for incorporating size restrictions [27], alternative metrics for denser subgraphs [13], evolving graphs [28], subgraphs with limited overlap [29], [30], and streaming or distributed settings [31], [32]. Dense subgraph detection has been applied to fraud detection in social or review networks [5], [12], [33], [34], [35].…”
Section: Related Workmentioning
confidence: 99%
“…Exact algorithms [14], [15] and approximate algorithms [10], [15] have been proposed for finding subgraphs with maximum average degree. These have been extended for incorporating size restrictions [27], alternative metrics for denser subgraphs [13], evolving graphs [28], subgraphs with limited overlap [29], [30], and streaming or distributed settings [31], [32]. Dense subgraph detection has been applied to fraud detection in social or review networks [5], [12], [33], [34], [35].…”
Section: Related Workmentioning
confidence: 99%
“…In many real applications, the objective is to find a set of cohesive subgraphs of the original input graph (rather than a single subgraph covering the input). Following the approach proposed in [11], this paper considers the problem of computing the set of largest k 2-clubs, with k ≥ 1. We will denote this problem as Top k-2-clubs.…”
Section: Iccs Camera Ready Version 2019mentioning
confidence: 99%
“…e problem of nding the top-k densest subgraph as sum of densities was shown to be NP-hard [6] and e cient heuristic was proposed to solve the problem. Further, Galbrun et al [17] studied the problem of nding the top-k overlapping densest subgraphs and provided constant-factor approximation guarantees.…”
Section: Related Workmentioning
confidence: 99%
“…In applications, we are o en interested not only in one densest subgraph, but in the top-k. e top-k densest subgraphs can be vertex-disjoint, edge-disjoint, or overlapping [6,17]. Di erent objective functions and constraints give rise to di erent problem formulations [6,17,32]. In this work, we choose to maximize the sum of the densities of the k subgraphs in the solution.…”
Section: Introductionmentioning
confidence: 99%