Percolation theory applied to measures of fragmentation in social networks
| dc.creator | Chen, Yiping | |
| dc.creator | Paul, Gerald | |
| dc.creator | Cohen, Reuven | |
| dc.creator | Havlin, Shlomo | |
| dc.creator | Borgatti, Stephen P. | |
| dc.creator | Liljeros, Fredrik | |
| dc.creator | Stanley, H. Eugene | |
| dc.date | 2006-10-23 | |
| dc.date.accessioned | 2026-07-07T07:56:23Z | |
| dc.date.available | 2026-07-07T07:56:23Z | |
| dc.description | 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, $P_{\infty}$, 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 Erdős-Rényi (ER) and scale-free (SF) 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, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ 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 $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results. | |
| dc.description | submitted to PRE | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0610625 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0610625 | |
| dc.identifier | Phys. Rev. E 75, 046107 (2007) | |
| dc.identifier | doi:10.1103/PhysRevE.75.046107 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127292 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Percolation theory applied to measures of fragmentation in social networks | |
| dc.type | text |