Topological graph clustering with thin position

TL;DR

This paper introduces a novel graph clustering algorithm inspired by topological thin position, aiming to improve the detection of tightly packed clusters in data represented as graphs.

Contribution

It presents a new clustering method leveraging topological concepts, specifically thin position, to identify highly connected subgraphs more effectively.

Findings

Demonstrates improved cluster detection in graph-structured data

Provides a topologically inspired approach to graph clustering

Shows potential advantages over traditional methods

Abstract

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a distance or similarity metric on the points, then look for highly connected subgraphs. We introduce such an algorithm based on ideas borrowed from the topological notion of thin position for knots and 3-dimensional manifolds.