Block Matrix Formulations for Evolving Networks

TL;DR

This paper introduces a block matrix approach to represent evolving networks over time, enabling the computation of dynamic centrality measures and improving numerical algorithms for analyzing temporal network data.

Contribution

It presents a novel block matrix formulation for evolving networks that captures temporal dynamics and enhances computational methods for centrality analysis.

Findings

Block matrix formulation accurately models temporal network evolution.

The approach enables computation of dynamic centrality measures respecting time order.

New algorithms derived from the formulation are more efficient for large networks.

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.