Bond percolation on a class of clustered random networks.

Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with nonzero clustering. The network's degree distribution and clustering spectrum may be prescribed and theoretical results match well with numerical simulations on both synthetic and real-world networks.

[1]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[2]  E. Volz,et al.  Random networks with tunable degree distribution and clustering. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M. Serrano,et al.  Percolation and epidemic thresholds in clustered networks. , 2006, Physical review letters.

[4]  P. Grassberger On the critical behavior of the general epidemic process and dynamical percolation , 1983 .

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

[6]  A. Arenas,et al.  Models of social networks based on social distance attachment. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  M. Newman Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[10]  Y. Moreno,et al.  Resilience to damage of graphs with degree correlations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[12]  Jean-Loup Guillaume,et al.  Bipartite graphs as models of complex networks , 2006 .

[13]  B. M. Fulk MATH , 1992 .

[14]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[15]  Marián Boguñá,et al.  Clustering in complex networks. II. Percolation properties. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Marián Boguñá,et al.  Tuning clustering in random networks with arbitrary degree distributions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[18]  M E J Newman,et al.  Random graphs with clustering. , 2009, Physical review letters.

[19]  Alessandro Vespignani,et al.  Large-scale topological and dynamical properties of the Internet. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Marián Boguñá,et al.  Clustering in complex networks. I. General formalism. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

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

[23]  James P. Sethna,et al.  Zero-temperature hysteresis in the random-field Ising model on a Bethe lattice , 1996 .

[24]  V. Eguíluz,et al.  Highly clustered scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  P. Trapman,et al.  On analytical approaches to epidemics on networks. , 2007, Theoretical population biology.

[26]  M. Newman Properties of highly clustered networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.