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Clique percolation

Béla Bollobás, Oliver Riordan
2009 Random structures & algorithms (Print)  
Derenyi, Palla and Vicsek introduced the following dependent percolation model, in the context of finding communities in networks.  ...  Starting with a random graph G generated by some rule, form an auxiliary graph G' whose vertices are the k-cliques of G, in which two vertices are joined if the corresponding cliques share k-1 vertices  ...  Variants In the rest of the paper we consider several variants of the clique percolation problem discussed above.  ... 
doi:10.1002/rsa.20270 fatcat:5jm7njovmjeulhrees2a7kffdm

k-Clique Percolation and Clustering [chapter]

Gergely Palla, Dániel Ábel, Illés J. Farkas, Péter Pollner, Imre Derényi, Tamás Vicsek
2008 Bolyai Society Mathematical Studies  
We summarise recent results connected to the concept of k-clique percolation.  ...  Finally, we demonstrate the effectiveness of k-clique percolation as a community finding method via a series of real-world applications.  ...  k-clique percolation cluster is negligible.  ... 
doi:10.1007/978-3-540-69395-6_9 fatcat:sesxqpbbknao7pnljyq45vlphy

Clique Percolation in Random Networks

Imre Derényi, Gergely Palla, Tamás Vicsek
2005 Physical Review Letters  
We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.  ...  The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated.  ...  A k-clique percolation cluster is very much like a regular (edge) percolation cluster in the k-clique adjacency graph, where the vertices represent the k-cliques of the original graph, and there is an  ... 
doi:10.1103/physrevlett.94.160202 pmid:15904198 fatcat:pca25s2cqzarhlk6twwqtccmaa

Clique percolation in random graphs

Ming Li, Youjin Deng, Bing-Hong Wang
2015 Physical Review E  
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k-cliques means that they share at least l1 makes a step-function-like  ...  All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.  ...  Obviously, the clique percolation in graph G corresponds to a normal percolation in graph G ′ .  ... 
doi:10.1103/physreve.92.042116 pmid:26565177 fatcat:3jtmvcfn75ahhengcqk436zsry

General Clique Percolation in Network Evolution [article]

Jingfang Fan, Xiaosong Chen
2013 arXiv   pre-print
The critical exponents of clique percolation depend on l, but are independent of k. The universality class of a (k,l) clique percolation is characterized alone by l.  ...  The emergence of a giant (k,l) clique community indicates a (k,l) clique percolation, which is studied by the largest size gap Δ of the largest clique community during network evolution and the corresponding  ...  The sequence of clique percolation in the ER model is as following: a) (2, 1) clique percolation at T c = 0.5N , b) (3, 1) clique percolation at T c = 0.5N 4/3 , c) (3, 2) clique percolation at T c = 2  ... 
arXiv:1309.4535v1 fatcat:bgpqwjxjtjexvdpse56ekznt6a

Sequential algorithm for fast clique percolation

Jussi M. Kumpula, Mikko Kivelä, Kimmo Kaski, Jari Saramäki
2008 Physical Review E  
Here we present a sequential clique percolation algorithm (SCP) to do fast community detection in weighted and unweighted networks, for cliques of a chosen size.  ...  In sparse weighted networks, the SCP algorithm can also be used for implementing the weighted clique percolation method recently introduced by Farkas et al.  ...  However, for intensity-based clique percolation this cannot be done, as all k-cliques have to be detected and sorted first. IV.  ... 
doi:10.1103/physreve.78.026109 pmid:18850899 fatcat:3ikocb4pljasfidviv3cu3gide

Exact formula for bond percolation on cliques

Peter Mann, V. Anne Smith, John B. O. Mitchell, Christopher Jefferson, Simon Dobson
2021 Physical review. E  
We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation.  ...  We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.  ...  We demonstrate that the percolation expression for these cycles is not readily obtained in closed form, unlike the expressions for simple cycles and cliques.  ... 
doi:10.1103/physreve.104.024304 fatcat:2zhr2b5i35ge7mpzj6otdcphz4

Clique percolation method: memory efficient almost exact communities [article]

Alexis Baudin, Maximilien Danisch, Sergey Kirgizov, Clémence Magnien, Marwan Ghanem
2021 arXiv   pre-print
The most popular method designed to find overlapping communities (where a node can belong to several communities) is perhaps the clique percolation method (CPM).  ...  This method formalizes the notion of community as a maximal union of k-cliques that can be reached from each other through a series of adjacent k-cliques, where two cliques are adjacent if and only if  ...  One of the most popular methods designed to find overlapping communities is the clique percolation method (cpm) which produces k-clique communities [14] . Definition 1 (k-clique).  ... 
arXiv:2110.01213v1 fatcat:zhcpu5lhhndb5hhojvmggrw7r4

Overlapping Modularity at the Critical Point of k-Clique Percolation

Bálint Tóth, Tamás Vicsek, Gergely Palla
2012 Journal of statistical physics  
In this approach the communities correspond to k-clique percolation clusters, and the general heuristic for setting the parameters of the method is to tune the system just below the critical point of k-clique  ...  percolation.  ...  We note that a k-clique percolation cluster is very much like a regular edge percolation cluster in the k-clique adjacency graph, where the nodes represent the k-cliques of the original network, and there  ... 
doi:10.1007/s10955-012-0640-5 fatcat:l5aypbx3h5fevcorwafdpzenvm

Clique-Attacks Detection in Web Search Engine for Spamdexing using K-Clique Percolation Technique

S. K. Jayanthi, S. Sasikala
2012 International Journal of Machine Learning and Computing  
This paper proposes a novel strategy to detect the spam based on K-Clique Percolation method. Data collected from website and classified with NaiveBayes Classification algorithm.  ...  Index Terms-Clique, link spam, search engine, ranking, search engine optimization.  ...  CONCLUSION TABLE I : I WEB SPAM LITERATURE REVIEW Clique-Attacks Detection in Web Search Engine for Spamdexing using K-Clique Percolation Technique S. K. Jayanthi and S.  ... 
doi:10.7763/ijmlc.2012.v2.207 fatcat:6sudph7iyzcslbvavuu7aysety

Natural Document Clustering by Clique Percolation in Random Graphs [chapter]

Wei Gao, Kam-Fai Wong
2006 Lecture Notes in Computer Science  
We propose a novel graph-theoretic technique called Clique Percolation Clustering (CPC).  ...  It models clustering as a process of enumerating adjacent maximal cliques in a random graph that unveils inherent structure of the underlying data, in which we unleash the commonly practiced constraints  ...  clusters (in dotted regions) Algorithm 2 . 2 Find All k-Clique Percolation Clusters input: A set of all maximal cliques MC and k. output: All k-clique percolation clusters into CP C. procedure Find-k-CPC  ... 
doi:10.1007/11880592_10 fatcat:fu6aytku3vahjoxse6fboh5cay

The Critical Point of k-Clique Percolation in the Erdős–Rényi Graph

Gergely Palla, Imre Derényi, Tamás Vicsek
2006 Journal of statistical physics  
Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph  ...  By making some assumptions that are expected to be valid below the threshold, we determine the average size of the k-clique percolation clusters, using a generating function formalism.  ...  k-clique percolation cluster is negligible.  ... 
doi:10.1007/s10955-006-9184-x fatcat:puspgbhn5fgmdiuevdv6bqozc4

Natural Emergence of a Core Structure in Networks via Clique Percolation

A. Melka, N. Slater, A. Mualem, Y. Louzoun
2019 Zenodo  
These percolating cliques produce a natural core and periphery structure. This result is generic and is tested in configuration models and in real-world networks.  ...  Multiple measures have been proposed for dense communities in graphs, the most classical being k-cliques, k-cores, and k-plexes, all presenting groups of tightly connected vertices.  ...  Cliques of size 2 percolate even a little before this threshold.  ... 
doi:10.5281/zenodo.3607830 fatcat:ynusicr2mjfjfg7fuompyr57by

K-clique percolation in free association networks. The mechanism behind the 7 ± 2 law ? [article]

Olga Valba, Alexander Gorsky
2021 arXiv   pre-print
Surprisingly it turned out that k-clique percolation for all k<k_c=(6-7) is possible on SWOW-EN and Dutch language network.  ...  In this study we discuss the k-clique percolation phenomenon on the free association networks including "English Small World of Words project" (SWOW-EN).  ...  K-clique percolation We begin with a few definitions laying down the fundamentals of k-clique percolation [16, 17] . K-clique is a complete (fully connected) subgraph of k vertices.  ... 
arXiv:2110.09317v1 fatcat:jc5htjai5fd3xjzbloqwljtsvq

Finding Collections of k-Clique Percolated Components in Attributed Graphs [chapter]

Pierre-Nicolas Mougel, Christophe Rigotti, Olivier Gandrillon
2012 Lecture Notes in Computer Science  
In this paper, we consider graphs where a set of Boolean attributes is associated to each vertex, and we are interested in k-clique percolated components (components made of overlapping cliques) in such  ...  We propose the task of finding the collections of homogeneous kclique percolated components, where homogeneity means sharing a common set of attributes having value true.  ...  A k-clique percolated component (termed also k-clique-community in [11] ) is a relaxed version of the concept of cliques.  ... 
doi:10.1007/978-3-642-30220-6_16 fatcat:tqq2de4gmje7filzoobprnijvm
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