Clustering Edges in Directed Graphs

TL;DR

This paper introduces a novel framework for edge clustering in directed graphs, enabling the identification of influence subgraphs by grouping edges with shared functional affinity, offering new insights into directed influence processes.

Contribution

It presents a new edge clustering framework with three spectral clustering methods, expanding analysis beyond traditional vertex clustering in directed graphs.

Findings

Edge clustering reveals influence subgraphs in directed graphs.

Three spectral clustering methods provide diverse insights into influence processes.

Framework is applicable to various scientific research domains.

Abstract

How do vertices exert influence in graph data? We develop a framework for edge clustering, a new method for exploratory data analysis that reveals how both vertices and edges collaboratively accomplish directed influence in graphs, especially for directed graphs. In contrast to the ubiquitous vertex clustering which groups vertices, edge clustering groups edges. Edges sharing a functional affinity are assigned to the same group and form an influence subgraph cluster. With a complexity comparable to that of vertex clustering, this framework presents three different methods for edge spectral clustering that reveal important influence subgraphs in graph data, with each method providing different insight into directed influence processes. We present several diverse examples demonstrating the potential for widespread application of edge clustering in scientific research.