Greedily Finding a Dense Subgraph

Asahiro, Yuichi; Iwama, Kazuo; Tamaki, Hisao; Tokuyama, Takeshi

doi:10.1006/jagm.1999.1062

Cited by 173 publications

(71 citation statements)

References 3 publications

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“…densest subgraph problem is to find subgraphs with a large average degree defined by ms ns . Asashiro et al propose a greedy algorithm to extract the densest subgraphs [4] and Charikar shows that this algorithm can run in linear time with approximation guarantees [7]. Besides, Tsourakakis et al define a novel density measurement as the edge surplus between the subgraph and the corresponding α-quasi-clique.…”

Section: Related Workmentioning

confidence: 99%

“…A major difference behind different dense subgraph detection techniques lies in the specific definition of the density. For example, [4] proposed a greedy algorithm to maximize the average degree ( 2ms n S ) and extract the densest subgraphs. Moreover, the edge surplus (i.e., the surplus between the number of edges in the extracted subgraph and its corresponding α-quasi-clique) is used to find a denser subgraph than the densest subgraph [24].…”

Section: Introductionmentioning

confidence: 99%

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HiDDen: Hierarchical Dense Subgraph Detection with Application to Financial Fraud Detection

Zhang¹,

Zhou²,

Yildirim³

et al. 2017

Proceedings of the 2017 SIAM International Conference on Data Mining

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Dense subgraphs are fundamental patterns in graphs, and dense subgraph detection is often the key step of numerous graph mining applications. Most of the existing methods aim to find a single subgraph with a high density. However, dense subgraphs at different granularities could reveal more intriguing patterns in the underlying graph. In this paper, we propose to hierarchically detect dense subgraphs. The key idea of our method (HiDDen) is to envision the density of subgraphs as a relative measure to its background (i.e., the subgraph at the coarse granularity). Given that the hierarchical dense subgraph detection problem is essentially a nonconvex quadratic programming problem, we propose effective and efficient alternative projected gradient based algorithms to solve it. The experimental evaluations on real graphs demonstrate that (1) our proposed algorithms find subgraphs with an up to 40% higher density in almost every hierarchy; (2) the densities of different hierarchies exhibit a desirable variety across different granularities; (3) our projected gradient descent based algorithm scales linearly w.r.t the number of edges of the input graph; and (4) our methods are able to reveal interesting patterns in the underlying graphs (e.g., synthetic ID in financial fraud detection).

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

HiDDen: Hierarchical Dense Subgraph Detection with Application to Financial Fraud Detection

Zhang¹,

Zhou²,

Yildirim³

et al. 2017

Proceedings of the 2017 SIAM International Conference on Data Mining

View full text Add to dashboard Cite

show abstract

“…The densest subgraph can be identified in polynomial time by solving a parametric maximum-flow problem [15]. Charikar [9] introduces a linear-programming formulation of the problem, while also showing that the greedy algorithm proposed by Asashiro et al [5] produces a 1 2 -approximation in linear time. The densest-subgraph problem has also been studied in a streaming context [6].…”

Section: Related Workmentioning

confidence: 99%

Finding Subgraphs with Maximum Total Density and Limited Overlap

Balalau

Bonchi

Chan

et al. 2015

Proceedings of the Eighth ACM International Conference on Web Search and Data Mining

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Finding dense subgraphs in large graphs is a key primitive in a variety of real-world application domains, encompassing social network analytics, event detection, biology, and finance. In most such applications, one typically aims at finding several (possibly overlapping) dense subgraphs which might correspond to communities in social networks or interesting events. While a large amount of work is devoted to finding a single densest subgraph, perhaps surprisingly, the problem of finding several dense subgraphs with limited overlap has not been studied in a principled way, to the best of our knowledge. In this work we define and study a natural generalization of the densest subgraph problem, where the main goal is to find at most k subgraphs with maximum total aggregate density, while satisfying an upper bound on the pairwise Jaccard coefficient between the sets of nodes of the subgraphs. After showing that such a problem is NP-Hard, we devise an efficient algorithm that comes with provable guarantees in some cases of interest, as well as, an efficient practical heuristic. Our extensive evaluation on large realworld graphs confirms the efficiency and effectiveness of our algorithms.

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“…Furthermore, there is a linear-time factor-2 approximation algorithm [6,16]. The algorithm deletes iteratively a vertex with the lowest degree, obtaining a sequence of subgraphs.…”

Section: Densest Subgraph Problemmentioning

confidence: 99%

Discovering Dynamic Communities in Interaction Networks

Rozenshtein

Tatti

Gionis

2014

Machine Learning and Knowledge Discovery in Databases

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Very often online social networks are defined by aggregating information regarding the interaction between the nodes of the network. For example, a call graph is defined by considering an edge for each pair of individuals who have called each other at least once -or at least k times. Similarly, an implicit social network in a social-media site is defined by considering an edge for each pair of users who have interacted in some way, e.g., have made a conversation, commented to each other's content, etc. Despite the fact that this type of definitions have been used to obtain a lot of insights regarding the structure of social networks, it is obvious that they suffer from a severe limitation: they neglect the precise time that the interaction between network nodes occurs.In this thesis we propose to study interaction networks, where one considers not only the underlying topology of the social network, but also the exact time instances that nodes interact. In an interaction network an edge is associated with a time stamp, and multiple edges may occur for the same pair of nodes. Consequently, interaction networks offer a more fine-grained representation that can be used to reveal otherwise hidden dynamic phenomena in the network.In the context of interaction networks, we study the problem of discovering communities, which are dense in terms of the underlying network structure, and whose edges occur in short time intervals. Such communities represent groups of individuals who interact with each other in some specific time instances, for example, a group of employees who work on a project and whose interaction intensifies before certain project milestones. We prove that the problem we define is NP-hard, and we provide effective algorithms by adapting techniques used to find dense subgraphs. We perform extensive evaluation of the proposed methods on synthetic and real datasets, which demonstrates the validity of our concepts and the good performance of our algorithms.

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Greedily Finding a Dense Subgraph

Cited by 173 publications

References 3 publications

HiDDen: Hierarchical Dense Subgraph Detection with Application to Financial Fraud Detection

HiDDen: Hierarchical Dense Subgraph Detection with Application to Financial Fraud Detection

Finding Subgraphs with Maximum Total Density and Limited Overlap

Discovering Dynamic Communities in Interaction Networks

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