Multiscale dynamical embeddings of complex networks
This work provides a novel framework for network analysis that bridges community detection and control theory, offering a principled way to extract reduced representations of complex networks.
The authors propose a time-dependent dynamical similarity measure for nodes in complex networks, derived from control theory, which enables dimensionality reduction and functional module detection. The method is demonstrated on directed and signed networks, showing its ability to capture multiscale dynamics.
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.