A geometric approach to robustness in complex networks

Gyan Ranjan, Zhi-Li Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We explore the geometry of networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L+). The reciprocal of squared distance from each node i to the origin in this n-dimensional space yields a structural centrality index (C*(i)) for the node, while the harmonic sum of individual node structural centrality indices, Σi 1/C* (i), i.e. the trace of L+, yields the well-known Kirchoff index (K), an overall structural descriptor for the network. In addition to its geometric interpretation, we provide alternative interpretation of the proposed structural centrality index (C*(i)) of each node in terms of forced detour costs and recurrences in random walks and electrical networks. Through empirical evaluation over example and real world networks, we demonstrate how structural centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchoff index, is appropriately sensitive to perturbations/rewirings in the network.

Original languageEnglish (US)
Title of host publicationProceedings - 31st International Conference on Distributed Computing Systems Workshops, ICDCSW 2011
Pages146-153
Number of pages8
DOIs
StatePublished - Sep 9 2011
Event31st International Conference on Distributed Computing Systems Workshops, ICDCSW 2011 - Minneapolis, MN, United States
Duration: Jun 20 2011Jun 24 2011

Publication series

NameProceedings - International Conference on Distributed Computing Systems

Other

Other31st International Conference on Distributed Computing Systems Workshops, ICDCSW 2011
CountryUnited States
CityMinneapolis, MN
Period6/20/116/24/11

Keywords

  • Complex networks
  • random walks
  • robustness
  • scale free networks

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