An Improved Node Ranking for Label Propagation and Modularity based Clustering

In this paper I’ll speak about non-spectral clustering techniques and see how a node ordering based on centrality measures can improve the quality of communities detected. I’ll also discuss an improvement to existing techniques, which further improves modularity.

💡 Research Summary

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The paper investigates how the order in which nodes are visited can influence the quality of community detection in two popular non‑spectral clustering algorithms: Label Propagation (LP) and the multilevel modularity‑maximization method introduced by Blondel et al. (often called the Louvain algorithm). Both algorithms iteratively update node labels or move nodes between clusters, and each iteration processes nodes in a predetermined sequence. While previous work has examined the effect of ordering for LP on unweighted graphs, the impact of node ordering on modularity‑based methods has received little attention.

To address this gap, the author proposes to order nodes according to various centrality measures, processing low‑centrality nodes first and high‑centrality nodes later. Four standard centralities are considered: (1) weighted degree (the sum of incident edge weights), (2) PageRank, (3) closeness (the inverse of the sum of shortest‑path distances to all other nodes), and (4) betweenness (the number of shortest paths that pass through a node). Because betweenness is an integer, many nodes can share the same value; to break ties the author introduces a “relative closeness” term C(v)=c(v)²/(2·maxₓc(x)+1), which lies in