Block Matrix Formulations for Evolving Networks
Copyright policy )Block Matrix Formulations for Evolving Networks
Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of adjacency matrices. We consider here the issue of representing the system as a single, higher dimensional block matrix, built from the individual time-slices. We focus on the task of computing network centrality measures. From a modeling perspective, we show that there is a suitable block formulation that allows us to recover dynamic centrality measures respecting time's arrow. From a computational perspective, we show that the new block formulation leads to the design of more effective numerical algorithms.
18 pages, 2 figures
- University of Pisa Italy
- University of Strathclyde United Kingdom
- University of Edinburgh United Kingdom
- University of Cagliari Italy
FOS: Computer and information sciences, Physics - Physics and Society, FOS: Physical sciences, Physics and Society (physics.soc-ph), 510, complex network, 05C50, 15A69, evolving network, Multilinear algebra, tensor calculus, FOS: Mathematics, centrality; complex network; evolving network; graph; tensor, Mathematics - Numerical Analysis, QA, Social and Information Networks (cs.SI), Graphs and linear algebra (matrices, eigenvalues, etc.), Computer Science - Social and Information Networks, centrality, Numerical Analysis (math.NA), graph, tensor, 004, Small world graphs, complex networks (graph-theoretic aspects), pairwise interactions, Mathematics
FOS: Computer and information sciences, Physics - Physics and Society, FOS: Physical sciences, Physics and Society (physics.soc-ph), 510, complex network, 05C50, 15A69, evolving network, Multilinear algebra, tensor calculus, FOS: Mathematics, centrality; complex network; evolving network; graph; tensor, Mathematics - Numerical Analysis, QA, Social and Information Networks (cs.SI), Graphs and linear algebra (matrices, eigenvalues, etc.), Computer Science - Social and Information Networks, centrality, Numerical Analysis (math.NA), graph, tensor, 004, Small world graphs, complex networks (graph-theoretic aspects), pairwise interactions, Mathematics
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