Dynamic Katz and Related Network Measures

TL;DR

This paper introduces a novel framework for dynamic walk-based centrality measures in time-ordered networks, emphasizing the computational advantages of dynamic Katz centrality and exploring walk combinatorics under backtracking constraints.

Contribution

It develops a method to compute dynamic Katz centrality efficiently at the node level and extends walk combinatorics to scenarios with backtracking restrictions.

Findings

Dynamic Katz centrality allows node-level computations.

Framework for walk combinatorics with backtracking constraints.

Analytic derivation of centrality measures for time-ordered networks.

Abstract

We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performed entirely at the node level. We then consider two distinct types of backtracking and develop a framework for capturing dynamic walk combinatorics when either or both is disallowed.