Dirichlet Graph Densifiers

摘要

In this paper, we propose a graph densification method based on minimizing the combinatorial Dirichlet integral for the line graph. This method allows to estimate meaningful commute distances for midsize graphs. It is fully bottom up and unsupervised, whereas anchor graphs, the most popular alternative, are top-down. Compared with anchor graphs, our method is very competitive (it is only outperformed for some choices of the parameters, namely the number of anchors). In addition, although it is not a spectral technique our method is spectrally well conditioned (spectral gap tends to be minimized). Finally, it does not rely on any pre-computation of cluster representatives.