Fast Node Vector Distance Computations using Laplacian Solvers

Abstract

Complex networks are a useful tool to investigate various phenomena in social science, economics, and logistics. Node Vector Distance (NVD) is an emerging set of techniques allowing us to estimate the distance and correlation between variables defined on the nodes of a network. One drawback of NVD is its high computational complexity. Here we show that a subset of NVD techniques, the ones calculating the Generalized Euclidean measure on networks, can be efficiently tackled with Laplacian solvers. In experiments, we show that this provides a significant runtime speedup with negligible approximation errors, which opens the possibility to scale the techniques to large networks.