Crossover phenomena of percolation transition in evolution networks with hybrid attachment

A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. For many real world networks, the mechanism of preferential attachment plays a significant role in the formation of heterogeneous structures, but the network percolation in evolution process with preferential attachment has not yet been concerned. We propose a tunable network percolation model by introducing a hybrid mechanism of edge selection into the Bohman-Frieze-Wormald model, in which a parameter adjusts the relative weights between random and preferential selections. A large number of simulations indicate that there exist crossover phenomena of percolation transition by adjusting the parameter in the evolution processes. When the strategy of selecting a candidate edge is dominated by random selection, a single discontinuous percolation transition occurs. When a candidate edge is selected more preferentially based on nodes degree, the size of the largest component undergoes multiple discontinuous jumps, which exhibits a peculiar difference from the network percolation of random selection with a certain restriction. Besides, the percolation transition becomes continuous when the candidate edge is selected completely preferentially.

[1]  N A M Araújo,et al.  Explosive percolation via control of the largest cluster. , 2010, Physical review letters.

[2]  Oliver Riordan,et al.  Explosive Percolation Is Continuous , 2011, Science.

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

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

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

[6]  Lazaros K. Gallos,et al.  Explosive percolation in the human protein homology network , 2009, 0911.4082.

[7]  Nong Ye,et al.  Propagation and immunization of infection on general networks with both homogeneous and heterogeneous components. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Abbas Ali Saberi,et al.  Recent advances in percolation theory and its applications , 2015, 1504.02898.

[9]  J. Rogers.  Chaos , 1876 .

[10]  Jari Saramäki,et al.  Using explosive percolation in analysis of real-world networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  L. Christophorou.  Science , 2018, Emerging Dynamics: Science, Energy, Society and Values.

[12]  Eric J Friedman,et al.  Construction and analysis of random networks with explosive percolation. , 2009, Physical review letters.

[13]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Wei Chen,et al.  Multiple discontinuous percolation transitions on scale-free networks , 2015 .

[15]  Marc Timme,et al.  Self-organized adaptation of a simple neural circuit enables complex robot behaviour , 2010, ArXiv.

[16]  Wei Chen,et al.  Explosive percolation with multiple giant components. , 2010, Physical review letters.

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

[18]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[19]  Roderich Moessner,et al.  Reversible first-order transition in Pauli percolation. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Ming Tang,et al.  Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks , 2015, Chaos.

[21]  K. Binder.  Finite size scaling analysis of ising model block distribution functions , 1981 .

[22]  Fredrik Liljeros,et al.  Preferential attachment in sexual networks , 2007, Proceedings of the National Academy of Sciences.

[23]  Cang Hui,et al.  Carrying capacity, population equilibrium, and environment's maximal load , 2006 .

[24]  B Kahng,et al.  Discontinuous percolation transitions in real physical systems. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[26]  G. Grimmett.  What Is Percolation , 1989 .

[27]  B. Kahng,et al.  Avoiding a Spanning Cluster in Percolation Models , 2013 .

[28]  R. Voss,et al.  The fractal dimension of percolation cluster hulls , 1984 .

[29]  B. Kahng,et al.  Percolation transitions in scale-free networks under the Achlioptas process. , 2009, Physical review letters.

[30]  Aonghus Lawlor,et al.  Tricritical point in heterogeneous k-core percolation. , 2011, Physical review letters.

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

[32]  Nong Ye,et al.  Connectivity distribution and attack tolerance of general networks with both preferential and random attachments , 2002 .

[33]  M. Newman.  Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  S. N. Dorogovtsev,et al.  Structure of growing networks with preferential linking. , 2000, Physical review letters.

[35]  José S Andrade,et al.  Tricritical point in explosive percolation. , 2010, Physical review letters.

[36]  Robert M Ziff,et al.  Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks. , 2009, Physical review letters.

[37]  J. Spencer,et al.  Explosive Percolation in Random Networks , 2009, Science.

[38]  Raissa M. D'Souza,et al.  Anomalous critical and supercritical phenomena in explosive percolation , 2015, Nature Physics.

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

[40]  F. Radicchi,et al.  Explosive percolation in scale-free networks. , 2009, Physical review letters.

[41]  Soon-Hyung Yook,et al.  Explosive percolation in a nanotube-based system. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

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

[44]  S. Havlin,et al.  Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition. , 2010, Physical review letters.

[45]  S N Dorogovtsev,et al.  Explosive percolation transition is actually continuous. , 2010, Physical review letters.

[46]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.

[47]  Beom Jun Kim,et al.  Continuity of the explosive percolation transition. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Wei Chen,et al.  Deriving an underlying mechanism for discontinuous percolation , 2011, 1106.2088.

[49]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[50]  M. Small,et al.  Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Thomas J. Fararo,et al.  A study of a biased friendship net , 1964 .

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

[53]  M. Small,et al.  Growing optimal scale-free networks via likelihood. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Derek de Solla Price,et al.  A general theory of bibliometric and other cumulative advantage processes , 1976, J. Am. Soc. Inf. Sci..

[55]  José S Andrade,et al.  Explosive electric breakdown due to conducting-particle deposition on an insulating substrate. , 2014, Physical review letters.

[56]  Peter Grassberger,et al.  Explosive percolation is continuous, but with unusual finite size behavior. , 2011, Physical review letters.

[57]  Judith L Bronstein,et al.  Population Dynamics and Mutualism: Functional Responses of Benefits and Costs , 2002, The American Naturalist.