Edge Sampling of Graphs Based on Edge Smoothness

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 important edges in the original graph. We present a general framework of edge sampling based on graph sampling theory and we also reveal a theoretical relationship between the original and line graphs. Experimental results in synthetic graphs validate the effectiveness of our approach against some alternative edge selection methods.