Percolation theory and fragmentation measures in social networks |
| |
Authors: | Yiping Chen Gerald Paul Reuven Cohen Shlomo Havlin Stephen P Borgatti Fredrik Liljeros H Eugene Stanley |
| |
Institution: | 1. Center for Polymer Studies, Boston University, Boston, MA 02215, USA;2. Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215, USA;3. Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel;4. Department of Org. Studies, Boston College, Chestnut Hill, MA 02467, USA;5. Department of Sociology, Stockholm University, S-106 91 Stockholm, Sweden |
| |
Abstract: | We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one traditionally used in percolation theory, P∞, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods, we study Erd?s–Rényi (ER) and scale-free (SF) networks under various node removal strategies. We find that for a network obtained after removal of a fraction q of nodes above criticality, P∞≈(1-F)1/2. For fixed P∞ and close to criticality, we show that 1-F better reflects the actual fragmentation. For a given P∞, 1-F has a broad distribution and thus one can improve significantly the fragmentation of the network. We also study and compare the fragmentation measure F and the percolation measure P∞ for a real national social network of workplaces linked by the households of the employees and find similar results. |
| |
Keywords: | Social network Fragmentation Percolation theory |
本文献已被 ScienceDirect 等数据库收录! |
|