Correlated edge overlaps in multiplex networks.

We develop the theory of sparse multiplex networks with partially overlapping links based on their local treelikeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find that correlations between the overlapping and nonoverlapping links markedly change the phase diagram of the system, leading to multiple hybrid phase transitions. For assortative correlations we observe recurrent hybrid phase transitions.

[1]  Dong Zhou,et al.  Percolation of interdependent networks with intersimilarity. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Xueqi Cheng,et al.  Unstable supercritical discontinuous percolation transitions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  G. Bianconi.  Statistical mechanics of multiplex networks: entropy and overlap. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[5]  Sangchul Lee,et al.  Link overlap, viability, and mutual percolation in multiplex networks , 2014, ArXiv.

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  Xueqi Cheng,et al.  Phase transitions in supercritical explosive percolation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  S. N. Dorogovtsev,et al.  Avalanche collapse of interdependent networks. , 2012, Physical review letters.

[9]  Pol Colomer-de-Simon,et al.  Double percolation phase transition in clustered complex networks , 2014, ArXiv.

[10]  Harold W. Gutch,et al.  Continuous Percolation with Discontinuities , 2012 .

[11]  Alexandre Arenas,et al.  Bond percolation on multiplex networks , 2015, ArXiv.

[12]  Ginestra Bianconi,et al.  Message passing theory for percolation models on multiplex networks with link overlap. , 2016, Physical review. E.

[13]  S. N. Dorogovtsev,et al.  Multiple percolation transitions in a configuration model of a network of networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  N Azimi-Tafreshi,et al.  Cooperative epidemics on multiplex networks. , 2015, Physical review. E.

[15]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[16]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[17]  Ginestra Bianconi,et al.  Percolation in multiplex networks with overlap. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Peter Grassberger,et al.  Percolation theory on interdependent networks based on epidemic spreading , 2011, 1109.4447.