Structure-Aware Distance Measures for Comparing Clusterings in Graphs

Clustering in graphs aims to group vertices with similar patterns of connections. Applications include discovering communities and latent structures in graphs. Many algorithms have been proposed to find graph clusterings, but an open problem is the need for suitable comparison measures to quantitatively validate these algorithms, performing consensus clustering and to track evolving (graph) clusters across time. To date, most comparison measures have focused on comparing the vertex groupings, and completely ignore the difference in the structural approximations in the clusterings, which can lead to counter-intuitive comparisons. In this paper, we propose new measures that account for differences in the approximations. We focus on comparison measures for two important graph clustering approaches, community detection and blockmodelling, and propose comparison measures that work for weighted (and unweighted) graphs.