Jamming in complex networks with degree correlation

Abstract We study the effects of the degree–degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally we apply our model to real world networks, and the results agree with our theoretical model.

[1]  Xiaoran Yan,et al.  Effects of degree correlation on scale-free gradient networks , 2010 .

[3]  M. di Bernardo,et al.  Synchronization in weighted scale-free networks with degree-degree correlation , 2006 .

[4]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[5]  H. Stanley,et al.  Structure of shells in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Sheng-Jun Wang,et al.  Effect of degree correlations on networked traffic dynamics , 2009 .

[7]  Haibo Hu,et al.  Disassortative mixing in online social networks , 2009, 0909.0450.

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

[9]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[10]  P. A. Macri,et al.  Using relaxational dynamics to reduce network congestion , 2008, 0803.3755.

[11]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Béla Bollobás,et al.  Random Graphs , 1985 .

[13]  Natali Gulbahce.  Optimization in gradient networks. , 2007, Chaos.

[14]  Alessandro Vespignani,et al.  Cut-offs and finite size effects in scale-free networks , 2003, cond-mat/0311650.

[15]  P. Macri,et al.  Discrete surface growth process as a synchronization mechanism for scale-free complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Kevin E. Bassler,et al.  Network dynamics: Jamming is limited in scale-free systems , 2004, Nature.

[17]  S N Dorogovtsev,et al.  Zero Pearson coefficient for strongly correlated growing trees. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Danuta Kiea,et al.  Acta Physica Polonica B , 2012 .

[19]  P A Macri,et al.  Evolution equation for a model of surface relaxation in complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  H. Stanley,et al.  Optimal paths in disordered complex networks. , 2003, Physical review letters.

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

[22]  Liang Li,et al.  Optimizing transport efficiency on scale-free networks through assortative or dissortative topology. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Y. Lai,et al.  Jamming in complex gradient networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  I. Sokolov,et al.  Reshuffling scale-free networks: from random to assortative. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[26]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[27]  Béla Bollobás,et al.  Random Graphs, Second Edition , 2001, Cambridge Studies in Advanced Mathematics.

[28]  Physics Letters , 1962, Nature.

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

[30]  J. Rogers.  Chaos , 1876 .

[31]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[32]  F. Family.  Scaling of rough surfaces: effects of surface diffusion , 1986 .

[33]  T. Mexia,et al.  Author ' s personal copy , 2009 .