Detecting community structure for undirected big graphs based on random walks

Community detection is a common problem in various types of big graphs. It is meaningful to understand the functions and dynamics of networks. The challenges of detecting community for big graphs include high computational cost, no prior information, etc.. In this work, we analyze the process of random walking in graphs, and find out that the weight of an edge gotten by processing the vertices visited by the walker could be an indicator to measure the closeness of vertex connection. Based on this idea, we propose a community detection algorithm for undirected big graphs which consists of three steps, including random walking using a single walker, weight calculating for edges and community detecting. Our algorithm is running in O(n2) without prior information. Experimental results show that our algorithm is capable of detecting the community structure and the overlapping parts of graphs in real-world effectively, and handling the challenges of community detection in big graph era.

[1]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[2]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[3]  Srinivasan Parthasarathy,et al.  Scalable graph clustering using stochastic flows: applications to community discovery , 2009, KDD.

[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]  Malik Magdon-Ismail,et al.  Defining and Discovering Communities in Social Networks , 2012 .

[6]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[7]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[8]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[9]  Matthieu Latapy,et al.  Computing Communities in Large Networks Using Random Walks , 2004, J. Graph Algorithms Appl..

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

[11]  Guy Shani,et al.  Evaluating Recommendation Systems , 2011, Recommender Systems Handbook.

[12]  Donald F. Towsley,et al.  Estimating and sampling graphs with multidimensional random walks , 2010, IMC '10.

[13]  Jure Leskovec,et al.  Information diffusion and external influence in networks , 2012, KDD.

[14]  David Harel,et al.  On Clustering Using Random Walks , 2001, FSTTCS.

[15]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[16]  M. Newman.  Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.