Model to Generate Benchmark Graphs Based on Evolution Dynamics

The past decade has seen tremendous growth in the field of Complex Social Networks. Several network generation models have been extensively studied to develop an understanding of how real world networks evolve over time. Two important applications of these models are to study the evolution dynamics and processes that shape a network, and to generate benchmark networks with known community structures. Research has been conducted in both these directions, relatively independent of the other. This creates a disjunct between real world networks and the networks generated as benchmarks to study community detection algorithms. In this paper, we propose to study both these application areas together. We introduce a network generation model which is based on evolution dynamics of real world networks and, it can generate networks with community structures that can be used as benchmark graphs. We study the behaviour of different community detection algorithms based on the proposed model and compare it with other models to generate benchmark graphs. Results suggest that the proposed model can generate networks which are not only structurally similar to real world networks but can be used to generate networks with varying community sizes and topologies.

[1]  Arnaud Sallaberry,et al.  Tunable and Growing Network Generation Model with Community Structures , 2013, 2013 International Conference on Cloud and Green Computing.

[2]  Yamir Moreno,et al.  The role of hidden influentials in the diffusion of online information cascades , 2013, EPJ Data Science.

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

[4]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[5]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  M. Newman Communities, modules and large-scale structure in networks , 2011, Nature Physics.

[8]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[9]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

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

[11]  Guy Melançon,et al.  Model for generating artificial social networks having community structures with small-world and scale-free properties , 2013, Social Network Analysis and Mining.

[12]  Xun Zhang,et al.  Growing community networks with local events , 2009, 0902.0652.

[13]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

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

[15]  Faraz Zaidi,et al.  Communities and hierarchical structures in dynamic social networks: analysis and visualization , 2011, Social Network Analysis and Mining.

[16]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[17]  Xiaofan Wang,et al.  A new community-based evolving network model , 2007 .

[18]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, KDD 2012.

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

[20]  Chien-Kuo Ku,et al.  A new scale-free network model for simulating and predicting epidemics. , 2013, Journal of theoretical biology.

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

[22]  Li Xiang,et al.  Weighted Evolving Networks with Self-organized Communities , 2008 .

[23]  Faraz Zaidi,et al.  Small world networks and clustered small world networks with random connectivity , 2012, Social Network Analysis and Mining.

[24]  Santo Fortunato,et al.  Community detection in networks: Structural communities versus ground truth , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Guy Melançon,et al.  Identifying the presence of communities in complex networks through topological decomposition and component densities , 2010, EGC.

[27]  S. Dongen Graph clustering by flow simulation , 2000 .

[28]  Bruce Edmonds,et al.  Towards Validating Social Network Simulations , 2013, ESSA.

[29]  B. Bollobás The evolution of random graphs , 1984 .

[30]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[32]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[34]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[35]  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.

[36]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[37]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[38]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Emilio Ferrara,et al.  A large-scale community structure analysis in Facebook , 2011, EPJ Data Science.

[40]  Guy Melançon,et al.  Continental integration in multilevel approach of world air transportation (2000-2004) , 2008 .