Grounding force-directed network layouts with latent space models

Abstract

Force-directed layout algorithms are ubiquitously-used tools for network visualization across a variety of scientific disciplines. However, they lack theoretical grounding which allows to interpret their outcomes rigorously. We propose an approach building on latent space network models, which assume that the probability of nodes forming a tie depends on their distance in an unobserved latent space. From such latent space models, we derive force equations for a force-directed layout algorithm.With this approach, force-directed layouts become interpretable, since the forces infer positions which maximize the likelihood of the given network under the latent space model. We implement these forces for (un)directed unweighted and weighted networks. We spatialise different real-world networks, where we find central network properties reflected in the layout, and compare the layouts to different force-directed algorithms already in use today. I. INTRODUCTIONThis contribution aims to bring together two strands of research: Latent space approaches to network analysis and force-directed layout algorithms (FDLs). FDLs are used ubiquitously for network exploration, illustration, and analysis in a wide variety of disciplines