Scale-Free Networks Emerging from Weighted Random Graphs
摘要
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is with . Our results imply that the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with . We show that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free ``supernode network''. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks.
引用
@article{arxiv.cond-mat/0503598,
title = {Scale-Free Networks Emerging from Weighted Random Graphs},
author = {Tomer Kalisky and Sameet Sreenivasan and Lidia A. Braunstein and Sergey V. Buldyrev and Shlomo Havlin and H. Eugene Stanley},
journal= {arXiv preprint arXiv:cond-mat/0503598},
year = {2015}
}