F\textsuperscript{2}LP-AP: Fast \& Flexible Label Propagation with Adaptive Propagation Kernel

TL;DR

F extsuperscript{2}LP-AP is a training-free, adaptive label propagation method that efficiently handles both homophilous and heterophilous graphs by adjusting to local topology, achieving high accuracy with low computational cost.

Contribution

It introduces a novel adaptive propagation kernel that dynamically adjusts based on local graph structure, improving flexibility and efficiency over existing methods.

Findings

F extsuperscript{2}LP-AP outperforms existing baselines in accuracy on benchmark datasets.

The method significantly reduces computational overhead compared to GNNs.

It effectively models heterophilous graphs without gradient-based training.

Abstract

Semi-supervised node classification is a foundational task in graph machine learning, yet state-of-the-art Graph Neural Networks (GNNs) are hindered by significant computational overhead and reliance on strong homophily assumptions. Traditional GNNs require expensive iterative training and multi-layer message passing, while existing training-free methods, such as Label Propagation, lack adaptability to heterophilo\-us graph structures. This paper presents \textbf{F$^2$LP-AP} (Fast and Flexible Label Propagation with Adaptive Propagation Kernel), a training-free, computationally efficient framework that adapts to local graph topology. Our method constructs robust class prototypes via the geometric median and dynamically adjusts propagation parameters based on the Local Clustering Coefficient (LCC), enabling effective modeling of both homophilous and heterophilous graphs without gradient-based training. Extensive experiments across diverse benchmark datasets demonstrate that \textbf{F$^2$LP-AP} achieves competitive or superior accuracy compared to trained GNNs, while significantly outperforming existing baselines in computational efficiency.