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Given a node-attributed graph, how can we efficiently represent it with fewnumerical features that expressively reflect its topology and attributeinformation? We propose A-DOGE, for Attributed DOS-based Graph Embedding, basedon density of states (DOS, a.k.a. spectral density) to tackle this problem.A-DOGE is designed to fulfill a long desiderata of desirable characteristics.Most notably, it capitalizes on efficient approximation algorithms for DOS,that we extend to blend in node labels and attributes for the first time,making it fast and scalable for large attributed graphs and graph databases.Being based on the entire eigenspectrum of a graph, A-DOGE can capturestructural and attribute properties at multiple ("glocal") scales. Moreover, itis unsupervised (i.e. agnostic to any specific objective) and lends itself tovarious interpretations, which makes it is suitable for exploratory graphmining tasks. Finally, it processes each graph independent of others, making itamenable for streaming settings as well as parallelization. Through extensiveexperiments, we show the efficacy and efficiency of A-DOGE on exploratory graphanalysis and graph classification tasks, where it significantly outperformsunsupervised baselines and achieves competitive performance with modernsupervised GNNs, while achieving the best trade-off between accuracy andruntime.

Fast Attributed Graph Embedding via Density of States