Measuring Similarity of Graphs and their Nodes by Neighbor Matching

TL;DR

This paper introduces a new neighbor-matching based method for measuring graph and node similarity, demonstrating its convergence and advantages over existing approaches through theoretical analysis and empirical comparison.

Contribution

A novel neighbor-matching similarity measure for graphs and nodes with proven convergence and improved properties over prior methods.

Findings

The proposed method converges reliably.

It exhibits desirable properties absent in previous measures.

Empirical results show competitive performance.

Abstract

The problem of measuring similarity of graphs and their nodes is important in a range of practical problems. There is a number of proposed measures, some of them being based on iterative calculation of similarity between two graphs and the principle that two nodes are as similar as their neighbors are. In our work, we propose one novel method of that sort, with a refined concept of similarity of two nodes that involves matching of their neighbors. We prove convergence of the proposed method and show that it has some additional desirable properties that, to our knowledge, the existing methods lack. We illustrate the method on two specific problems and empirically compare it to other methods.