Block Matrix Formulations for Evolving Networks

Caterina Fenu; Desmond J. Higham

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arXiv · 1511.07305

Block Matrix Formulations for Evolving Networks

Caterina Fenu·Desmond J. Higham

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Abstract

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.

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Caterina Fenu, Desmond J. Higham. 2016-06-01. Block Matrix Formulations for Evolving Networks. https://arxiv.org/abs/1511.07305

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