Robust Node Affinities via Jaccard-Biased Random Walks and Rank Aggregation

TL;DR

This paper introduces TopKGraphs, a novel method for estimating node similarity in networks using biased random walks and rank aggregation, providing an interpretable and robust alternative to existing techniques.

Contribution

TopKGraphs is a new non-parametric approach that biases random walks towards structurally similar nodes and aggregates partial rankings to produce interpretable node affinity matrices.

Findings

TopKGraphs outperforms standard similarity measures in various network scenarios.

The method is robust in sparse, noisy, and heterogeneous networks.

It provides a versatile, interpretable alternative to embedding-based similarity approaches.

Abstract

Estimating node similarity is a fundamental task in network analysis and graph-based machine learning, with applications in clustering, community detection, classification, and recommendation. We propose TopKGraphs, a method based on start-node-anchored random walks that bias transitions toward nodes with structurally similar neighborhoods, measured via Jaccard similarity. Rather than computing stationary distributions, walks are treated as stochastic neighborhood samplers, producing partial node rankings that are aggregated using robust rank aggregation to construct interpretable node-to-node affinity matrices. TopKGraphs provides a non-parametric, interpretable, and general-purpose representation of node similarity that can be applied in both network analysis and machine learning workflows. We evaluate the method on synthetic graphs (stochastic block models, Lancichinetti-Fortunato-Radicchi benchmark graphs), k-nearest-neighbor graphs from tabular datasets, and a curated high-confidence protein-protein interaction network. Across all scenarios, TopKGraphs achieves competitive or superior performance compared to standard similarity measures (Jaccard, Dice), a diffusion-based method (personalized PageRank), and an embedding-based approach (Node2Vec), demonstrating robustness in sparse, noisy, or heterogeneous networks. These results suggest that TopKGraphs is a versatile and interpretable tool for bridging simple local similarity measures with more complex embedding-based approaches, facilitating both data mining and network analysis applications.