Enhanced Flow in SmallWorld Networks
Abstract
The proper addition of shortcuts to a regular substrate can lead to the formation of a complex network with a highly efficient structure for navigation [J. M. Kleinberg, Nature 406, 845 (2000)]. Here we show that enhanced flow properties can also be observed in these smallworld topologies. Precisely, our model is a network built from an underlying regular lattice over which longrange connections are randomly added according to the probability, P_{ij}∼r_{ijα, where rij} is the Manhattan distance between nodes i and j, and the exponent α is a controlling parameter. The mean twopoint global conductance of the system is computed by considering that each link has a local conductance given by g_{ij}∝ri_{j}^{C}, where C determines the extent of the geographical limitations (costs) on the longrange connections. Our results show that the best flow conditions are obtained for C =0 with α=0, while for C≫1 the overall conductance always increases with α. For C≈1, α=d becomes the optimal exponent, where d is the topological dimension of the substrate. Interestingly, this exponent is identical to the one obtained for optimal navigation in smallworld networks using decentralized algorithms.
 Publication:

Physical Review Letters
 Pub Date:
 April 2014
 DOI:
 10.1103/PhysRevLett.112.148701
 arXiv:
 arXiv:1309.0040
 Bibcode:
 2014PhRvL.112n8701O
 Keywords:

 89.75.Hc;
 02.50.r;
 05.60.Cd;
 Networks and genealogical trees;
 Probability theory stochastic processes and statistics;
 Classical transport;
 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society
 EPrint:
 doi:10.1103/PhysRevLett.112.148701