TY - GEN
T1 - A geometric approach to robustness in complex networks
AU - Ranjan, Gyan
AU - Zhang, Zhi-Li
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Complex networks
KW - random walks
KW - robustness
KW - scale free networks
UR - http://www.scopus.com/inward/record.url?scp=80052402571&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052402571&partnerID=8YFLogxK
U2 - 10.1109/ICDCSW.2011.18
DO - 10.1109/ICDCSW.2011.18
M3 - Conference contribution
AN - SCOPUS:80052402571
SN - 9780769543864
T3 - Proceedings - International Conference on Distributed Computing Systems
SP - 146
EP - 153
BT - Proceedings - 31st International Conference on Distributed Computing Systems Workshops, ICDCSW 2011
T2 - 31st International Conference on Distributed Computing Systems Workshops, ICDCSW 2011
Y2 - 20 June 2011 through 24 June 2011
ER -