Dynamical Systems to Monitor Complex Networks in Continuous Time

TL;DR

This paper introduces a continuous-time dynamical systems approach to monitor and identify influential nodes in evolving networks using new Katz-style centrality measures derived from nonautonomous ODEs, enabling real-time analysis.

Contribution

The paper develops a novel continuous-time Katz-style centrality framework based on nonautonomous ODEs, allowing dynamic influence tracking in evolving networks.

Findings

New centrality measures effectively identify influential nodes in real-time.

Tracking receivers is computationally cheaper than tracking broadcasters.

Application to large voice call networks reveals key features not seen in static analysis.

Abstract

In many settings it is appropriate to treat the evolution of pairwise interactions over continuous time. We show that new Katz-style centrality measures can be derived in this context via solutions to a nonautonomous ODE driven by the network dynamics. This allows us to identify and track, at any resolution, the most influential nodes in terms of broadcasting and receiving information through time dependent links. In addition to the classical notion of attenuation across edges used in the static Katz centrality measure, the ODE also allows for attenuation over time, so that real time "running measures" can be computed. With regard to computational efficiency, we explain why it is cheaper to track good receivers of information than good broadcasters. We illustrate the new measures on a large scale voice call network, where key features are discovered that are not evident from snapshots or aggregates.