Cascades on a class of clustered random networks

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in [M. E. J. Newman, Phys. Rev. Lett. 103, 058701 (2009)]. A condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase, or decrease, the expected cascade size. Applications, examples of which are provided, include site percolation, bond percolation, and Watts' threshold model; in all cases analytical results give excellent agreement with numerical simulations.

[1]  Sergey N. Dorogovtsev,et al.  k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  J. Coleman.  Rationality and Society , 1989 .

[3]  Mark E. J. Newman,et al.  Random graphs containing arbitrary distributions of subgraphs , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[5]  K. Eames,et al.  Modelling disease spread through random and regular contacts in clustered populations. , 2008, Theoretical population biology.

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

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

[8]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[9]  M E J Newman,et al.  Component sizes in networks with arbitrary degree distributions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  R. Pastor-Satorras,et al.  Critical load and congestion instabilities in scale-free networks , 2003 .

[11]  Julio M. Ottino,et al.  Complex networks , 2004, Encyclopedia of Big Data.

[12]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[13]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[14]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

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

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

[17]  K. Goh,et al.  Robustness of the avalanche dynamics in data-packet transport on scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Takehisa Hasegawa,et al.  Cascade dynamics on clustered network , 2010 .

[19]  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.

[20]  Joel C. Miller,et al.  Percolation and epidemics in random clustered networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  D. Watts,et al.  Influentials, Networks, and Public Opinion Formation , 2007 .

[22]  F. Ball,et al.  Analysis of a stochastic SIR epidemic on a random network incorporating household structure. , 2010, Mathematical biosciences.

[23]  J. Gleeson,et al.  Seed size strongly affects cascades on random networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  S. Melnik,et al.  Analytical results for bond percolation and k-core sizes on clustered networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Remo Guidieri.  Res , 1995, RES: Anthropology and Aesthetics.

[27]  Joel C. Miller.  Spread of infectious disease through clustered populations , 2008, Journal of The Royal Society Interface.

[28]  James P Gleeson,et al.  Mean size of avalanches on directed random networks with arbitrary degree distributions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Shore,et al.  Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations. , 1992, Physical review letters.

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

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

[32]  Béla Bollobás,et al.  A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs , 1980, Eur. J. Comb..

[33]  S. N. Dorogovtsev,et al.  Bootstrap percolation on complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Andreas N. Lagerås,et al.  Epidemics on Random Graphs with Tunable Clustering , 2007, Journal of Applied Probability.

[35]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[36]  Sergey Melnik,et al.  How clustering affects the bond percolation threshold in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[39]  Massimo Marchiori,et al.  Model for cascading failures in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  L. Hébert-Dufresne,et al.  Propagation dynamics on networks featuring complex topologies. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  D. Watts,et al.  Social Influence, Binary Decisions and Collective Dynamics , 2008 .

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

[43]  Prabodh Shukla.  Driven Random Field Ising Model: some exactly solved examples in threshold activated kinetics , 2003 .

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

[45]  Deok-Sun Lee,et al.  Cascading toppling dynamics on scale-free networks , 2005 .

[46]  Edward A. Bender,et al.  The Asymptotic Number of Labeled Graphs with Given Degree Sequences , 1978, J. Comb. Theory A.

[47]  Sergey N. Dorogovtsev,et al.  K-core Organization of Complex Networks , 2005, Physical review letters.

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

[49]  Ying-Cheng Lai,et al.  Complex networks: Dynamics and security , 2005 .

[50]  B. M. Fulk.  MATH , 1992 .

[51]  Zhong Chen,et al.  Efficient target strategies for contagion in scale-free networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  S Redner,et al.  Evolutionary dynamics on degree-heterogeneous graphs. , 2006, Physical review letters.

[53]  B Kahng,et al.  Sandpile on scale-free networks. , 2003, Physical review letters.

[54]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[55]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[56]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[58]  James P Gleeson,et al.  Bond percolation on a class of clustered random networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.