Scale-free networks emerging from weighted random graphs

Tomer Kalisky, Sameet Sreenivasan, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin, H. Eugene Stanley
2006 Physical Review E  
We study Erdös-Rényi 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 P(k)∼ k^-λ with λ=2.5. 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
more » ... hat create a scale-free tree with λ=2.5. 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.
doi:10.1103/physreve.73.025103 pmid:16605380 fatcat:wsv7u3uyqfhppbiy5cecujhtgm