Optimal modularity in complex contagion

In this chapter, we apply the theoretical framework introduced in the previous chapter to study how the modular structure of the social network affects the spreading of complex contagion. In particular, we focus on the notion of optimal modularity, that predicts the occurrence of global cascades when the network exhibits just the right amount of modularity. Here we generalize the findings by assuming the presence of multiple communities and a uniform distribution of seeds across the network. Finally, we offer some insights into the temporal evolution of cascades in the regime of the optimal modularity.

[1]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  James P Gleeson,et al.  Cascades on correlated and modular random networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[4]  Alessandro Flammini,et al.  Optimal network clustering for information diffusion , 2014, Physical review letters.

[5]  Matthias Bethge,et al.  Statistical Analysis of Multi-Cell Recordings: Linking Population Coding Models to Experimental Data , 2011, Front. Comput. Neurosci..

[6]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[7]  Changsong Zhou,et al.  Sustained Activity in Hierarchical Modular Neural Networks: Self-Organized Criticality and Oscillations , 2010, Front. Comput. Neurosci..

[8]  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.

[9]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[10]  Filippo Menczer,et al.  Virality Prediction and Community Structure in Social Networks , 2013, Scientific Reports.

[11]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[12]  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.

[13]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.