Using Cliques with Higher-order Spectral Embeddings Improves Graph Visualizations

Abstract

In the simplest setting, graph visualization is the problem of producing a set of two-dimensional coordinates for each node that meaningfully shows connections and latent structure in a graph. Among other uses, having a meaningful layout is often useful to help interpret the results from network science tasks such as community detection and link prediction. There are several existing graph visualization techniques in the literature that are based on spectral methods, graph embeddings, or optimizing graph distances. Despite the large number of methods, it is still often challenging or extremely time consuming to produce meaningful layouts of graphs with hundreds of thousands of vertices. Existing methods often either fail to produce a visualization in a meaningful time window, or produce a layout colorfully called a "hairball", which does not illustrate any internal structure in the graph. Here, we show that adding higher-order information based on cliques to a classic eigenvector based graph visualization technique enables it to produce meaningful plots of large graphs. We further evaluate these visualizations along a number of graph visualization metrics and we find that it outperforms existing techniques on a metric that uses random walks to measure the local structure. Finally, we show many examples of how our algorithm successfully produces layouts of large networks. Code to reproduce our results is available.