Grounding force-directed network layouts with latent space models

Abstract

Force-directed layout algorithms are ubiquitously-used tools for network visualisation across a multitude of scientific disciplines. However, they lack theoretical grounding which allows to interpret their outcomes rigorously and can guide the choice of specific algorithms for certain data sets. We propose an approach building on latent space 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. Since the forces infer positions which maximise the likelihood of the given network under the latent space model, the force-directed layout becomes interpretable. We implement these forces for unweighted and weighted networks and spatialise different real-world networks. Comparison to existing layout algorithms (not grounded in an interpretable model) reveals that node groups are placed in similar configurations, while said algorithms show a stronger intra-cluster separation of nodes, as well as a tendency to separate clusters more strongly in retweet networks. We also explore the possibility of visualising data traditionally not seen as network data, such as survey data.