Identifying Modules in Complex Networks by a Graph-Theoretical Method and Its Application in Protein Interaction Networks

Detecting community structure/modules in complex networks recently attracts increasing attention from various fields including mathematics, physics and biology. In this paper, we propose a method based on graph-theoretical clustering for identifying modularity structure in complex networks. Compared with the existing algorithms, this method, based on minimum spanning tree, has several advantages. For example, unlike many algorithms, this method is deterministic and not sensitive to the initialization. In addition, the method does not require a prior knowledge about the number of the modules. It can easily obtain the number of clusters by analyzing the edge weight distribution of minimum spanning tree. Moreover, this algorithm has computational compexity of polynomial-time with low order and can be used to deal with large-scale networks. Experimental results show that our method produces good results for real networks and can also uncover meaningful functional modules in protein interaction networks.

[1]  Stefan Bornholdt,et al.  Detecting fuzzy community structures in complex networks with a Potts model. , 2004, Physical review letters.

[2]  Ruiqi Wang,et al.  Modelling periodic oscillation of biological systems with multiple timescale networks. , 2004, Systems biology.

[3]  Trupti Joshi,et al.  Inferring gene regulatory networks from multiple microarray datasets , 2006, Bioinform..

[4]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  P. Bork,et al.  Proteome survey reveals modularity of the yeast cell machinery , 2006, Nature.

[6]  Agnes Vathy-Fogarassy,et al.  Minimal Spanning Tree based Fuzzy Clustering , 2007 .

[7]  J. Gower,et al.  Minimum Spanning Trees and Single Linkage Cluster Analysis , 1969 .

[8]  Shi-Hua Zhang,et al.  A Graph-Theoretic Method for Mining Functional Modules in Large Sparse Protein Interaction Networks , 2006, Sixth IEEE International Conference on Data Mining - Workshops (ICDMW'06).

[9]  Siëlle Gramser.  Fake pottery buries theory of early start for Christianity , 2005, Nature.

[10]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[11]  Ying Xu,et al.  A segmentation algorithm for noisy images: Design and evaluation , 1998, Pattern Recognit. Lett..

[12]  Jon M. Kleinberg,et al.  Inferring Web communities from link topology , 1998, HYPERTEXT '98.

[13]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

[14]  Ciro Cattuto,et al.  Proceedings of the 20th ACM conference on Hypertext and hypermedia , 2009 .

[15]  Niina Päivinen.  Clustering with a minimum spanning tree of scale-free-like structure , 2005, Pattern Recognit. Lett..

[16]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Ying Xu,et al.  Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees , 2002, Bioinform..

[18]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[19]  Padhraic Smyth,et al.  A Spectral Clustering Approach To Finding Communities in Graph , 2005, SDM.

[20]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[21]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[22]  Dmitrij Frishman,et al.  MIPS: a database for genomes and protein sequences , 1999, Nucleic Acids Res..

[23]  Luonan Chen,et al.  Inferring protein interactions from experimental data by association probabilistic method , 2006, Proteins.

[24]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[25]  Tamás Vicsek,et al.  Phase transitions and overlapping modules in complex networks , 2007 .

[26]  Shi-Hua Zhang,et al.  Identification of functional modules in a PPI network by clique percolation clustering , 2006, Comput. Biol. Chem..

[27]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[28]  Richard Simon,et al.  Iterative class discovery and feature selection using Minimal Spanning Trees , 2004, BMC Bioinformatics.

[29]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Mika Gustafsson,et al.  Comparison and validation of community structures in complex networks , 2006 .

[31]  A. Arenas,et al.  Community detection in complex networks using extremal optimization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  S Boccaletti,et al.  Identification of network modules by optimization of ratio association. , 2006, Chaos.