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Percolation theory applied to measures of fragmentation in social networks
Phys. Rev. E (2007)
  • Yiping Chen, Boston University
  • Gerald Paul, Boston University
  • Reuven Cohen, Boston University
  • Shlomo Havlin, Bar-Ilan University, Israel
  • Stephen P. Borgatti, Boston College
  • Fredrik Liljeros
  • Eugene Stanley, Boston University
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∞, 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 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∞≈(1−F)1∕2. For fixed P∞ and close to percolation threshold (q=qc), we show that 1−F better reflects the actual fragmentation. Close to qc, for a given P∞, 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∞ for a real social network of workplaces linked by the households of the employees and find similar results.
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Citation Information
Yiping Chen, Gerald Paul, Reuven Cohen, Shlomo Havlin, et al.. "Percolation theory applied to measures of fragmentation in social networks" Phys. Rev. E Vol. 75 Iss. 4 (2007)
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