Multiscale dynamical embeddings of complex networks

TL;DR

This paper introduces a time-dependent dynamical similarity measure for complex networks, enabling low-dimensional embeddings that capture multi-scale dynamics and facilitate functional module detection, inspired by Control Theory.

Contribution

It proposes a novel dynamical similarity measure and embedding method for complex networks, linking community detection with Control Theory concepts.

Findings

Effective dimensionality reduction across multiple time scales

Uncovering functional modules using dynamical embeddings

Generalization of community detection methods

Abstract

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from Control Theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i)~dimensionality reduction, i.e., projecting nodes onto a low dimensional space that captures dynamic similarity at different time scales, and (ii)~how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity, and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to Control Theory, by using the here developed dynamical perspective.