Fig. 5
From: Non-backtracking cycles: length spectrum theory and graph mining applications
Different ways of comparing non-backtracking eigenvalues. We compare the non-backtracking eigenvalues of two different graphs of the same data set using three different methods: EMD, Euclidean, Hausdorff (see “Choice of distance and dependence on r” section), using the r eigenvalues largest in magnitude. We also show the median value r0 after which the eigenvalues have magnitude less than \(\sqrt {\lambda _{1}}\). Shaded areas show standard deviation. First two rows show results for random graphs of models KR and HG for different number of nodes n. Bottom row shows results for real data sets. See Table 2 for description of data sets. Values have been normalized by the largest observed distance with each different distance method for ease of comparison