Graph Comparison Based on Adjacency Function Matrix

TL;DR

This paper introduces a novel metric for comparing large graphs based on adjacency information, capable of handling graphs with different node set sizes, enhancing structural similarity analysis.

Contribution

The paper proposes a new graph distance metric utilizing adjacency functions that works for graphs of different sizes, unlike existing methods.

Findings

Effective comparison of large graphs with different node counts.

New metric captures structural similarities based on adjacency information.

Applicable to diverse graph analysis tasks.

Abstract

In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all vertices in the graph. Then, we defined a new function and some parameters to find the distance of two large graphs using different neighbors of vertices. There are some methods which they focused on the other features of graphs to obtain the distance between them, but some of them are Node Correspondence which means their node set have the same size. However, in this paper, we introduce a new method which can find the distance between two large graphs with different size of node set.