Sequential algorithm for fast clique percolation

Abstract

In complex network research clique percolation, introduced by Palla, Derényi, and Vicsek [Nature (London) 435, 814 (2005)], is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network. 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. This method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure. Unlike existing algorithms, the SCP method allows for detecting k -clique communities at multiple weight thresholds in a single run, and can simultaneously produce a dendrogram representation of hierarchical community structure. In sparse weighted networks, the SCP algorithm can also be used for implementing the weighted clique percolation method recently introduced by Farkas [New J. Phys. 9, 180 (2007)]. The computational time of the SCP algorithm scales linearly with the number of k -cliques in the network. As an example, the method is applied to a product association network, revealing its nested community structure.

Application of a K-Ladder Connectivity Algorithm for Clustering of Protein Evolutionary Network

“…cliques), the advantage of the basic algorithm in speed and scalability are dramatically lost. For example, processing according to the clique percolation approach [16], [17] takes several hours for clustering, while the basic k-ladder approach takes only about a minute.…”

“…We chose to use an extreme case of this connectivity definition, where the connected elements of the 'ladder' are considered cliques of a certain selected size, and the condition for their connection is the existence of a chosen amount of common nodes. Such an approach was suggested in [16] as percolation of cliques [16], [17]. (1) -connected components of the primary graph after "pre-clustering" and filtering; (2), (3) -bi-and tri-connected components of the largest component of (1); (4), (5) -bi-and tri-connected components of the second largest component of (1); (6), (7) -3-ladder connected components of the first two largest components of (1); 9 10 50 64 61 40 27 20 18 16 16 15 14 60 147 134 64 55 45 34 28 27 26 24 70 285 283 119 93 60 58 47 46 35 29 75 798 297 117 64 47 37 35 30 28 26 80 1409 166 48 42 41 40 31 30 25 24 A drawback of the "cliques" method is a very high level of overlapping of the clusters that makes it difficult to accurately interpret the results.…”

“…cliques), the advantage of the basic algorithm in speed and scalability are dramatically lost. For example, processing according to the clique percolation approach [16], [17] takes several hours for clustering, while the basic k-ladder approach takes only about a minute.Another problem of the application of k-ladder connectivity clustering to dense networks is the possibility of high overlapping between the resulting clusters.Although in the initial K-ladder approach there is a possibility for a node to belong to several clusters, the meaning of a connecting edge is unique. This is not the case when the unit is more complicated than cycle and connection rule requires more than just a common edge.…”

A Fast Method of Detecting Overlapping Community in Network Based on LFM

“…Similar methods include [11], [12]; Methods based on label propagation [13] firstly allocated a single label to each node ,And then update the label and membership degree of each node according to its neighbor nodes .finally , nodes owning the same label will be divided to the same community ,and those nodes who has more than one labels will be overlapping nodes .Methods based on edges [14] build line graph in which the node comes from the edge in original graph .then it use a non-overlapping community detection method to process the line graph ,as one node can belong to several edges ,thus ,it detect overlapping communities successfully. Methods based using the fitness function (such as LFM [15], DEMON [16], OSLM [17]) assume that the communities are local structures, which comprise of the nodes of the modules themselves and the extension to the nodes in its neighborhood.…”

A Novel Genetic Algorithm for Overlapping Community Detection

“…There are other algorithms for overlapping community detection,such that the SCP of Kumpula [10], Lancichinetti's algorithm [7], etc. All of them need prior information, or have coverage problem, or suffer of efficiency.…”