Kalisky Tomer, Sreenivasan Sameet, Braunstein Lidia A, Buldyrev Sergey V, Havlin Shlomo, Stanley H Eugene
Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Feb;73(2 Pt 2):025103. doi: 10.1103/PhysRevE.73.025103. Epub 2006 Feb 10.
We study Erdös-Rényi random graphs with random weights associated with each link. We generate a "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 P(k) approximately k(-lambda) with lambda=2.5. Our results imply that the minimum spanning tree in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with lambda=2.5. We suggest 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.
我们研究了具有与每条边相关联的随机权重的厄多斯-雷尼随机图。通过将由权重低于渗流阈值的边连接的所有节点（渗流簇）合并为一个单一节点，我们生成了一个“超节点网络”。我们表明，该网络是无标度的，即度分布为(P(k)\approx k^{-\lambda})，其中(\lambda = 2.5)。我们的结果意味着随机图中的最小生成树由渗流簇组成，这些渗流簇通过一组边相互连接，形成了一个(\lambda = 2.5)的无标度树。我们认为优化会使渗流阈值自发出现，从而自然地创建一个无标度超节点网络。我们讨论了这种现象与几个现实世界无标度网络的演化相关的可能性。
