A fast and complete algorithm for enumerating pseudo-cliques in large graphs

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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“…A variant of the k-plex can be found in Zhai et al [29], who add further connectivity constraints called CLB.…”

Section: Efficient Clique Enumerationmentioning

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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“…For cliques, an example is the work by Zhou et al for finding the top-k cliques [26]. Zhai et al [25], rather than aiming for large sized solutions, define a new pseudo-clique structure, similar to the k-plex, where small solutions are allowed as long as they are dense enough. Behar and Cohen [2] also aim at finding large pseudo cliques using a different model, that is connected s-cliques.…”

Section: Related Workmentioning

confidence: 99%

D2k

Conte

Matteis

Sensi

et al. 2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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This paper studies k-plexes, which are arguably the most popular pseudo-clique model for network communities. In a k-plex, each node can miss at most k − 1 links. Our goal is to detect large communities in today's real-world graphs which can have hundreds of millions of edges. While many have tried, this task has been elusive so far due to its computationally challenging nature: k-plexes and other pseudo-cliques are harder to find and more numerous than cliques, a well known hard problem. We present d2k, which is the first algorithm able to find large k-plexes of very large graphs in just a few minutes. The good performance of our algorithm follows from a combination of graph-theoretical concepts, careful algorithm engineering and a high-performance implementation. In particular, we exploit the low degeneracy of real-world graphs, and the fact that large enough k-plexes have diameter 2. We validate a sequential and a parallel/distributed implementation of d2k on real graphs with up to half a billion edges.

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“…Other quasi clique models include the one de ned by Zhai et al [21], that is a k-plex with additional connectivity constraint (called CLB), and more that can be found in this survey by Pa illo et al [16].…”

Section: Related Workmentioning

confidence: 99%

“…Some [7,11] have proposed decomposition approaches to limit the memory usage, as this allows in-memory computation on larger instances, and can provide a speedup even when the graph ts in main memory. Others, such as Zhai et al [21], exploit properties speci c to the considered quasi-cliuque model to prune the search space.…”

Section: Related Workmentioning

confidence: 99%

Fast Enumeration of Large k-Plexes

Conte

Firmani

Mordente³

et al. 2017

Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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k-plexes are a formal yet exible way of de ning communities in networks. ey generalize the notion of cliques and are more appropriate in most real cases: while a node of a clique C is connected to all other nodes of C, a node of a k-plex may miss up to k connections. Unfortunately, computing all maximal k-plexes is a gruesome task and state-of-the-art algorithms can only process small-size networks. In this paper we propose a new approach for enumerating large k-plexes in networks that speeds up the search by several orders of magnitude, leveraging on (i) methods for strongly reducing the search space and (ii) e cient techniques for the computation of maximal cliques. Several experiments show that our strategy is e ective and is able to increase the size of the networks for which the computation of large k-plexes is feasible from a few hundred to several hundred thousand nodes.

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A fast and complete algorithm for enumerating pseudo-cliques in large graphs

Cited by 8 publications

References 26 publications

A meta-algorithm for finding large k-plexes

A meta-algorithm for finding large k-plexes

D2k

Fast Enumeration of Large k-Plexes

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