Enhanced Flow in Small-World 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 small-world topologies. Precisely, our model is a network built from an underlying regular lattice over which long-range connections are randomly added according to the probability, Pij∼rij-α, where rij is the Manhattan distance between nodes i and j, and the exponent α is a controlling parameter. The mean two-point global conductance of the system is computed by considering that each link has a local conductance given by gij∝rij-C, where C determines the extent of the geographical limitations (costs) on the long-range 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 small-world 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
- E-Print:
- doi:10.1103/PhysRevLett.112.148701