Low-rank Similarity Measure for Role Model Extraction

Computing meaningful clusters of nodes is crucial to analyze large networks. In this paper, we present a pairwise node similarity measure that allows to extract roles, i.e. group of nodes sharing similar flow patterns within a network. We propose a low rank iterative scheme to approximate the similarity measure for very large networks. Finally, we show that our low rank similarity score successfully extracts the different roles in random graphs and that its performances are similar to the pairwise similarity measure.

[1]  Alex Arenas,et al.  Analysis of the structure of complex networks at different resolution levels , 2007, physics/0703218.

[2]  J. Huisman.  The Netherlands , 1996, The Lancet.

[3]  J. Reichardt,et al.  Statistical mechanics of community detection. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Thomas P. Cason,et al.  Role extraction in networks , 2012 .

[5]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

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

[7]  Mauricio Barahona,et al.  Finding role communities in directed networks using Role-Based Similarity, Markov Stability and the Relaxed Minimum Spanning Tree , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[8]  G. Stewart.  Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

[9]  Douglas R. White,et al.  Role models for complex networks , 2007, 0708.0958.

[10]  Paul Van Dooren,et al.  A MEASURE OF SIMILARITY BETWEEN GRAPH VERTICES . WITH APPLICATIONS TO SYNONYM EXTRACTION AND WEB SEARCHING , 2002 .

[11]  Mason A. Porter,et al.  Communities in Networks , 2009, ArXiv.

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

[13]  Arnaud Browet,et al.  Fast community detection using local neighbourhood search , 2013, ArXiv.

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

[15]  Mauricio Barahona,et al.  Role-similarity based comparison of directed networks , 2011, ArXiv.

[16]  Jari Saramäki,et al.  Model of community emergence in weighted social networks , 2009, Comput. Phys. Commun..

[17]  Jean-Charles Delvenne,et al.  Markov Dynamics as a Zooming Lens for Multiscale Community Detection: Non Clique-Like Communities and the Field-of-View Limit , 2011, PloS one.