# Quantum walk inspired algorithm for graph similarity and isomorphism

## TL;DR

This paper introduces a quantum walk inspired algorithm that efficiently measures graph similarity and distinguishes structural differences in large, unlabeled graphs with polynomial complexity, addressing scalability issues in network analysis.

## Contribution

The paper presents a novel quantum walk inspired algorithm for graph similarity that operates without prior graph labeling and has polynomial complexity.

## Key findings

- Capable of distinguishing minor structural differences in graphs
- Operates efficiently on large graphs with polynomial complexity
- Provides a scalable solution for graph comparison without prior labeling

## Abstract

Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity between network graphs in order to make quantitative comparisons. Since these networks can be very large, scalability and efficiency of the algorithm are key concerns. More importantly, for graphs with unknown labeling, this graph similarity problem requires exponential time to solve using existing algorithms. In this paper, we propose a quantum walk inspired algorithm, which provides a solution to the graph similarity problem without prior knowledge on graph labeling. This algorithm is capable of distinguishing between minor structural differences, such as between strongly regular graphs with the same parameters. The algorithm has polynomial complexity, scaling with $O(n^9)$.