Parallelizing maximal clique and k-plex enumeration over graph data

Wang, Zhuo; Chen, Qun; Hou, Boyi; Suo, Bo; Li, Zhanhuai; Pan, Wei

doi:10.1016/j.jpdc.2017.03.003

Cited by 27 publications

(18 citation statements)

References 35 publications

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“…Applications to different systems, in which larger plexes are required, may require additional development. Along this line, maximal k-plex identification, which is a computationally costly algorithm at the core of DPPM, has received renewed interest in network sciences, which could lead to further speed improvements 49,50 .…”

Section: Discussionmentioning

confidence: 99%

Robust dynamic community detection with applications to human brain functional networks

Martinet

Viles

et al. 2020

Nat Commun

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While current technology permits inference of dynamic brain networks over long time periods at high temporal resolution, the detailed structure of dynamic network communities during human seizures remains poorly understood. We introduce a new methodology that addresses critical aspects unique to the analysis of dynamic functional networks inferred from noisy data. We propose a dynamic plex percolation method (DPPM) that is robust to edge noise, and yields well-defined spatiotemporal communities that span forward and backwards in time. We show in simulation that DPPM outperforms existing methods in accurately capturing certain stereotypical dynamic community behaviors in noisy situations. We then illustrate the ability of this method to track dynamic community organization during human seizures, using invasive brain voltage recordings at seizure onset. We conjecture that application of this method will yield new targets for surgical treatment of epilepsy, and more generally could provide new insights in other network neuroscience applications.

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Section: Discussionmentioning

confidence: 99%

Robust dynamic community detection with applications to human brain functional networks

Martinet

Viles

et al. 2020

Nat Commun

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“…In this section we evaluate the performance of our method d2k with respect to the competitors gp [22] and lp [9] using the graphs in Table 1(a) and (b) when generating 2-plexes and 3-plexes of size at least q. All the methods were run in a sequential setting.…”

Section: Performance Evaluationmentioning

confidence: 99%

“…While the original version [6] does not provide any guarantee, the version in [18] guarantees a total running time of O(3 n/3 ), which worstcase-optimal, and the one in [12] further improves the work for sparse graphs, which may have up to (n − d)3 d /3 maximal cliques, by producing an algorithm with O(d(n −d)3 d /3 ) time. This strategy has been adapted to the enumeration of maximal k-plexes in [23], and inspired the similar backtracking structure in [22].…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we focus on k-plexes, arguably the most popular notion of pseudo-cliques [3,9,16,22,23]: the requirement of each node being linked to all others is loosened to each node missing no more than k − 1 links or, equivalently, missing k links including the one to itself (absence self-loops is assumed). Some examples are shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…While computation of cliques on large and sparse real-world networks is feasible with ad-hoc algorithms [10,12], computing k-plexes on such networks has been so far a task out of reach: [9] finds the largest 2-plex on a graph with 1.8 million edges, and [22] scales up to a graph with 22 million edges (see pokec in Table 1), but only processes a subgraph made by 10 of its nodes and the surrounding areas.…”

Section: Introductionmentioning

confidence: 99%

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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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Parallelizing maximal clique and k-plex enumeration over graph data

Cited by 27 publications

References 35 publications

Robust dynamic community detection with applications to human brain functional networks

Robust dynamic community detection with applications to human brain functional networks

D2k

Business Network Analytics: From Graphs to Supernetworks

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