Scale-free networks emerging from weighted random graphs.
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.
Kalisky
Tomer
T
Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel. kaliskt@mail.biu.ac.il
Sreenivasan
Sameet
S
Braunstein
Lidia A
LA
Buldyrev
Sergey V
SV
Havlin
Shlomo
S
Stanley
H Eugene
HE