Eigenvector Centrality in Highly Partitioned Mobile Networks: Principles and Applications

Abstract

Summary. In this chapter we introduce a model for analyzing the spread of epidemics in a disconnected mobile network. The work is based on an extension, to a dynamic setting, of the eigenvector centrality principle introduced by two of the authors for the case of static networks. The extension builds on a new definition of connectivity matrix for a highly partitioned mobile system, where the connectivity between a pair of nodes is defined as the number of contacts taking place over a finite time window. The connectivity matrix is then used to evaluate the eigenvector centrality of the various nodes. Numerical results from real-world traces are presented and discussed. The applicability of the proposed approach to select on-line message forwarders is also addressed.

Transient Dynamics of Epidemic Spreading and Its Mitigation on Large Networks

“…To avoid the triviality, we exclude the trivial cases x(t 0 ) = 0 and x(t 0 ) = 1 throughout the paper. 6 Thus, there is at least one node i having strictly positive probability of being infected at time t 0 , i.e.,…”

“…Therefore, the conventional use of the EVC [5,6,39,45] to characterize the SI epidemic dynamics and its applications to identify critical nodes for vaccine allocation become largely questionable. This also calls for a more precise approximate solution of (2) that works for any arbitrary x(t 0 ) over a longer period of time t, which will lead to more effective policies for combating the epidemics and providing vaccine distribution.…”

Graph spectral techniques in computer sciences

“…Google's PageRank is a variant of the eigenvector centrality measure. For more details, see [20,21].…”

“…The transformation I − Graph spectral techniques in computer sciences 21 We have seen how a vector x can be transformed to a scalar multiple of j using the iteration process (1), which involves the Laplacian matrix of the multiprocessor graph G. It remains to be seen what relations (1) mean in terms of load moving.…”

Determining Asset Criticality for Cyber Defense

“…to identify key entities/individuals in a network [25]. The widely used measures of centrality are degree centrality, betweenness, closeness, and eigenvector centrality [26]. In fact, the PageRank algorithm mentioned previously is a variation of eigenvector centrality.…”