NetKI: A kirchhoff index based statistical graph embedding in nearly linear time

Abstract

Recent advancements in learning from graph-structured data have shown promising results on the graph classification task. However, due to their high time complexities, making them scalable on large graphs, with millions of nodes and edges, remains a challenge. In this paper, we propose NetKI, an algorithm to extract sparse representation from a given graph with n nodes and m edges in O(m∊-2log4n) time. Our approach follows the notion of Kirchhoff index that encodes the structure of the graph by estimating effective resistance - relying on this approach yields nearly linear time graph representation method that allows scalability on sufficiently large graphs. Through extensive experiments, we show that NetKI provides improved results in terms of running time on large networks and the classification accuracy is within range 2% from the state-of-the-art results.