Edge Sampling of Graphs: Graph Signal Processing Approach With Edge Smoothness

TL;DR

This paper introduces a graph signal processing-based framework for identifying important edges by converting the graph to a line graph and sampling based on edge smoothness, validated through experiments.

Contribution

It presents a novel edge sampling method using graph sampling theory and establishes a theoretical link between the original and line graph degrees.

Findings

Effective edge importance identification demonstrated in synthetic graphs.

Outperforms alternative edge selection methods in real-world data.

Acceleration technique improves sampling efficiency.

Abstract

Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on graphs. We convert the original graph to a line graph where its nodes and edges, respectively, represent the original edges and the connections between the edges. We then perform node sampling of the line graph based on the edge smoothness assumption: This process selects the most critical edges in the original graph. We present a general framework of edge sampling based on graph sampling theory and reveal a theoretical relationship between the degree of the original graph and the line graph. We also propose an acceleration method for edge sampling in the proposed framework by using the relationship between two types of Laplacian of the node and edge domains. Experimental results in synthetic and real-world graphs validate the effectiveness of our approach against some alternative edge selection methods.