Analyzing the Small World Phenomenon Using a Hybrid Model with Local Network Flow

摘要

Randomly generated graphs with power law degree distribution are typically used to model large real-world networks. These graphs have small average distance. However, the small world phenomenon includes both small average distance and the clustering effect, which is not possessed by random graphs. Here we use a hybrid model which combines a global graph (a random power law graph) with a local graph (a graph with high local connectivity defined by network flow). We present an efficient algorithm which extracts a local graph from a given realistic network. We show that the hybrid model is robust in the sense that for any graph generated by the hybrid model, the extraction algorithm approximately recovers the local graph.