Katz Centrality of Markovian Temporal Networks: Analysis and Optimization

TL;DR

This paper extends Katz centrality to Markovian temporal networks using system theory, enabling efficient computation and optimization of node importance in dynamic networks.

Contribution

It introduces a novel generalization of Katz centrality for Markovian temporal networks and develops efficient computation and optimization methods.

Findings

Katz centrality can be computed via linear programming.

The proposed optimization improves node importance in temporal networks.

Numerical simulations validate the effectiveness of the methods.

Abstract

Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools in the context of temporal networks (i.e., networks whose connectivity dynamically changes over time). The aim of this paper is to propose a system-theoretic approach for identifying important nodes in temporal networks. In this direction, we first propose a generalization of the popular Katz centrality measure to the family of Markovian temporal networks using tools from the theory of Markov jump linear systems. We then show that Katz centrality in Markovian temporal networks can be efficiently computed using linear programming. Finally, we propose a convex program for optimizing the Katz centrality of a given node by tuning the weights of the temporal network in a cost-efficient manner. Numerical simulations illustrate the effectiveness of the obtained results.