Clique Relaxation Models in Social Network Analysis

Pattillo, Jeffrey; Youssef, Nataly; Butenko, Sergiy

doi:10.1007/978-1-4614-0857-4_5

Cited by 48 publications

(18 citation statements)

References 62 publications

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“…A formal and strict way of defining a community is the clique, a set of nodes in a network connected by all possible edges among them. However, it has been observed that cliques are too rigid to use in practice [22]. A more appropriate notion in many practical cases is the k-plex: a set of nodes such that each of them is linked to all the others, except at most k. For example, for k = 1, k-plexes are cliques as each node misses only the link to itself, for k = 2, each node may miss the link to one neighbor (and itself), and so on.…”

Section: Introductionmentioning

confidence: 99%

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A meta-algorithm for finding large k-plexes

et al. 2021

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We focus on the automatic detection of communities in large networks, a challenging problem in many disciplines (such as sociology, biology, and computer science). Humans tend to associate to form families, villages, and nations. Similarly, the elements of real-world networks naturally tend to form highly connected groups. A popular model to represent such structures is the clique, that is, a set of fully interconnected nodes. However, it has been observed that cliques are too strict to represent communities in practice. The k-plex relaxes the notion of clique, by allowing each node to miss up to k connections. Although k-plexes are more flexible than cliques, finding them is more challenging as their number is greater. In addition, most of them are small and not significant. In this paper we tackle the problem of finding only large k-plexes (i.e., comparable in size to the largest clique) and design a meta-algorithm that can be used on top of known enumeration algorithms to return only significant k-plexes in a fraction of the time. Our approach relies on: (1) methods for strongly reducing the search space and (2) decomposition techniques based on the efficient computation of maximal cliques. We demonstrate experimentally that known enumeration algorithms equipped with our approach can run orders of magnitude faster than full enumeration.

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Section: Introductionmentioning

confidence: 99%

“…The problem of finding k-plexes arises in several application domains, including social network analysis [2] and more in general graph-based data mining [5,22,29]. Unfortunately, (a) 2-plex, s=6…”

Section: Introductionmentioning

confidence: 99%

A meta-algorithm for finding large k-plexes

et al. 2021

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“…where w V : V → R and w E : E → R are the weight functions for the vertices and edges respectively. Successfully solving the MWC problem has various applications not only in computer vision [17,12] but in many different domains from wireless to social networks [21,19]. The main contributions of our paper include:…”

Section: Introductionmentioning

confidence: 99%

Common Object Discovery as Local Search for Maximum Weight Cliques in a Global Object Similarity Graph

Rao

Fan

et al. 2019

Discrete Geometry for Computer Imagery

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In this paper, we consider the task of discovering the common objects in a set of images. Initially, object candidates are generated in each image and an undirected weighted graph is constructed over all the candidates. Each candidate serves as a node in the graph while the weight of the edge describes the similarity between the corresponding pair of candidates. The problem is then expressed as a search for the Maximum Weight Clique (MWC) in this graph. The MWC corresponds to a set of object candidates sharing maximal mutual similarity, and each node in the MWC represents a discovered common object class across the images. Since the problem of finding MWCs is NP-hard, the research of the MWC problem focuses on developing various heuristics for finding good cliques within a reasonable time limit. We utilize a recently very popular class of heuristics called local search methods. They search for MWCs directly in the discrete domain of the solution space. The proposed approach is evaluated on the PASCAL VOC image dataset and the YouTube-Objects video dataset, and it demonstrates superior performance over recent state-of-the-art approaches.

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“…Early applications can be found for instance in Ballard & Brown (1982); Barahona, Weintraub, & Epstein (1992) and Christofides (1975) and are surveyed in Bomze, Budinich, Pardalos, & Pelillo (1999) and Pardalos & Xue (1994). Nowadays, more and more practical applications of clique problems arise in a number A C C E P T E D M A N U S C R I P T of domains including bioinformatics and chemoinformatics (Dognin, Andonov, & Yanev, 2010;Ravetti & Moscato, 2008), coding theory (Etzion &Östergård, 1998), economics (Boginski, Butenko, & Pardalos, 2006), examination planning (Carter, Laporte, & Lee, 1996;Carter & Johnson, 2001), financial networks (Boginski, Butenko, & Pardalos, 2006), location (Brotcorne, Laporte, & Semet, 2002), scheduling (Dorndorf, Jaehn, & Pesch, 2008;Weide, Ryan, & Ehrgott, 2010), signal transmission analysis (Chen, Zhai, & Fang, 2010), social network analysis (Balasundaram, Butenko, & Hicks, 2011;Pattillo, Youssef, & Butenko, 2012), wireless networks and telecommunications (Balasundaram, & Butenko, 2006;Jain, Padhye, Padmanabhan, & Qiu, 2005). In addition to these applications, the MCP is tightly related to some important combinatorial optimization problems such as clique partitioning (Wang, Alidaee, Glover, & Kochenberger, 2006), graph clustering (Schaeffer, 2007), graph vertex coloring (Chams, Hertz, & Werra, 1987;Wu & Hao, 2012a), max-min diversity (Croce, Grosso, & Locatelli, 2009), optimal winner determination (Shoham, Cramton, & Steinberg, 2006;Wu & Hao, 2015), set packing (Wu, Hao, & Glover, 2012) and sum coloring …”

Section: Introductionmentioning

confidence: 99%

A review on algorithms for maximum clique problems

Hao

2015

European Journal of Operational Research

262

168

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The maximum clique problem (MCP) is to determine in a graph a clique (i.e., a complete subgraph) of maximum cardinality. The MCP is notable for its capability of modeling other combinatorial problems and real-world applications. As one of the most studied NP-hard problems, many algorithms are available in the literature and new methods are continually being proposed. Given that the two existing surveys on the MCP date back to 1994 and 1999 respectively, one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic MCP algorithms, with a special focus on recent developments. To be informative, we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the most relevant clique methods, this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches.

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Clique Relaxation Models in Social Network Analysis

Cited by 48 publications

References 62 publications

A meta-algorithm for finding large k-plexes

A meta-algorithm for finding large k-plexes

Common Object Discovery as Local Search for Maximum Weight Cliques in a Global Object Similarity Graph

A review on algorithms for maximum clique problems

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