Dynamic networks and directed percolation
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the evolution of the network in time. We show that the dynamic network...
Saved in:
Published in | arXiv.org |
---|---|
Main Authors | , , , , |
Format | Paper Journal Article |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
01.02.2009
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the evolution of the network in time. We show that the dynamic network undergoes a percolation phase transition at a critical concentration \(p_c\), which decreases with the rate \(r\) at which the network links are changed. The behavior near criticality is universal and independent of \(r\). We find fundamental network laws are changed. (i) For Erdős-R\'{e}nyi networks we find that the size of the giant component at criticality scales with the network size \(N\) for all values of \(r\), rather than as \(N^{2/3}\). (ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as \(N^{1/2}\), compared to \(N^{1/3}\) in a static network. |
---|---|
ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.0901.4563 |