Morphological organization of point-to-point transport in complex networks

We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied, selects two tree-like structures, one emerging from the source and the other converging to the drain. These trees merge into a large cluster of the remaining nodes that is found to be quasi-equipotential and thus presents almost no resistance to transport. Such a global “tree-cluster-tree” structure is universal and leads to a power law decay of the currents distribution. Its exponent, −2, is determined by the multiplicative decrease of currents at successive branching points of a tree and is found to be independent of the network connectivity degree and resistance distribution.

[1]  Ginestra Bianconi,et al.  Scale-free networks with an exponent less than two. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  J. Klafter,et al.  First-passage times in complex scale-invariant media , 2007, Nature.

[3]  B. Sapoval,et al.  Diffusion-reaction in branched structures: theory and application to the lung acinus. , 2005, Physical review letters.

[4]  Hans J. Herrmann,et al.  Revealing the structure of the world airline network , 2014, Scientific Reports.

[5]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[6]  Marta C. González,et al.  A Metric of Influential Spreading during Contagion Dynamics through the Air Transportation Network , 2012, PloS one.

[7]  R. Pastor-Satorras,et al.  Generation of uncorrelated random scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  S. Havlin,et al.  Scaling theory of transport in complex biological networks , 2007, Proceedings of the National Academy of Sciences.

[9]  Reuven Cohen,et al.  Complex Networks: Structure, Robustness and Function , 2010 .

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

[11]  Ruben Juanes,et al.  Anomalous physical transport in complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Sinan Aral,et al.  Exercise contagion in a global social network , 2017, Nature Communications.

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

[14]  Dan Hu,et al.  Adaptation and optimization of biological transport networks. , 2013, Physical review letters.

[15]  J. Brasington,et al.  Let's get connected: A new graph theory‐based approach and toolbox for understanding braided river morphodynamics , 2018, WIREs Water.

[16]  Christos Nicolaides,et al.  Anomalous transport in complex networks , 2011 .

[17]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Shlomo Havlin,et al.  Anomalous transport in scale-free networks. , 2005, Physical review letters.

[19]  Harry Eugene Stanley,et al.  Transport in networks with multiple sources and sinks , 2008, ArXiv.

[20]  H E Stanley,et al.  Towards design principles for optimal transport networks. , 2010, Physical review letters.

[21]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[22]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .

[23]  J. Stoyanov.  A Guide to First‐passage Processes , 2003 .

[24]  A. Maritan,et al.  Evolution and selection of river networks: Statics, dynamics, and complexity , 2014, Proceedings of the National Academy of Sciences.

[25]  Guido Caldarelli,et al.  Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science , 2007 .

[26]  D. Grebenkov.  What makes a boundary less accessible. , 2005, Physical review letters.

[27]  Hawoong Jeong,et al.  Classification of scale-free networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Alexander Blumen,et al.  Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks , 2011, 1101.2572.

[29]  Erik M. Bollt,et al.  What is Special about Diffusion on Scale-Free Nets? , 2004 .

[30]  Francis Corson,et al.  Fluctuations and redundancy in optimal transport networks. , 2009, Physical review letters.

[31]  S. N. Dorogovtsev,et al.  Pseudofractal scale-free web. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[33]  Filippo Radicchi,et al.  Beyond the locally treelike approximation for percolation on real networks. , 2016, Physical review. E.

[34]  Hernán A. Makse,et al.  A review of fractality and self-similarity in complex networks , 2007 .

[35]  Emilio Hernández-García,et al.  Chemical and Biological Processes in Fluid Flows: A Dynamical Systems Approach , 2009 .

[36]  M. Barthelemy.  Betweenness centrality in large complex networks , 2003, cond-mat/0309436.