2006/10/23 by Yi‐Ping Phoebe Chen, Yiping Chen, Gerald Paul +5 · 3 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.75.046107
published as Phys. Rev. E 75, 046107 (2007) · submitted to PRE
arxiv created 2006/10/23 · openalex publication_date 2007/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We apply percolation theory to a recently proposed measure of fragmentation F for social networks. The measure F is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction q of nodes and the total number of pairs in the original fully connected network. We compare F with the traditional measure used in percolation theory, P(infinity), the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erdos-Rényi and scale-free networks under various types of node removal strategies. The removal strategies are random removal, high degree removal, and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction q of nodes above percolation threshold, P(infinity) approximately (1-F)1/2. For fixed P(infinity) and close to percolation threshold (q=qc), we show that 1-F better reflects the actual fragmentation. Close to qc, for a given P(infinity), 1-F has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure F and the percolation measure P(infinity) for a real social network of workplaces linked by the households of the employees and find similar results.