Fig. 1
From: Non-backtracking cycles: length spectrum theory and graph mining applications
Non-backtracking eigenvalues of random graphs. Left: From six different random graph models – Erdös-Rényi (ER), Barabási-Albert (BA), Stochastic Kronecker Graphs (KR), Configuration Model with power law degree distribution (CM), Watts-Strogatz (WS), Hyperbolic Graphs (HG) – we generate 50 graphs. From each of those 300 (=6×50) graphs, we plot the largest r=200 non-backtracking eigenvalues on the complex plane. To make the plot more readable, we show only eigenvalues close to the origin. All graphs have n=5×104 nodes and average degree approximately 〈k〉=15. Right: For each graph used in the left panel, we take its eigenvalues as a high-dimensional feature vector and apply UMAP over this set of 300 vectors to compute a 2-dimensional projection. For UMAP, we use a neighborhood of 75 data points and Canberra distance to get a more global view of the data set