Consistency between ordering and clustering methods for graphs

TL;DR

This paper explores the relationship between clustering and ordering methods for graph data, introducing a measure to quantify their consistency and evaluating their performance on synthetic and real datasets.

Contribution

It investigates the methodological links between spectral clustering and ordering methods, and proposes a new measure called label continuity error.

Findings

Ordering methods can identify module structures effectively.

Clustering methods can detect banded structures.

The proposed measure quantifies consistency between ordering and clustering.

Abstract

A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has been studied much more actively than the latter, particularly for the data represented as graphs. This study fills this gap by investigating methodological relationships between several clustering and ordering methods, focusing on spectral techniques. Furthermore, we evaluate the resulting performance of the clustering and ordering methods. To this end, we propose a measure called the label continuity error, which generically quantifies the degree of consistency between a sequence and partition for a set of elements. Based on synthetic and real-world datasets, we evaluate the extents to which an ordering method identifies a module structure and a clustering method identifies a banded structure.