Node Centrality Approximation For Large Networks Based On Inductive Graph Neural Networks

TL;DR

The paper addresses the high computational cost of CC and BC on large networks by reframing node ranking as a machine-learning task. It introduces CNCA-IGE, an inductive encoder–decoder architecture that uses GraphSAGE or VGAE for node embeddings and a downstream MLP or MLP-Mixer to predict CC/BC rankings, achieving faster inference with robust performance. Empirical results on synthetic and real networks show superior accuracy and a 25–30% speedup over baselines, with the MLP-Mixer decoder particularly improving robustness for BC ranking. This approach enables scalable, generalizable centrality ranking suitable for large-scale and evolving networks, with potential extensions to directed weighted and temporal graphs.

Abstract

Closeness Centrality (CC) and Betweenness Centrality (BC) are crucial metrics in network analysis, providing essential reference for discerning the significance of nodes within complex networks. These measures find wide applications in critical tasks, such as community detection and network dismantling. However, their practical implementation on extensive networks remains computationally demanding due to their high time complexity. To mitigate these computational challenges, numerous approximation algorithms have been developed to expedite the computation of CC and BC. Nevertheless, even these approximations still necessitate substantial processing time when applied to large-scale networks. Furthermore, their output proves sensitive to even minor perturbations within the network structure. In this work, We redefine the CC and BC node ranking problem as a machine learning problem and propose the CNCA-IGE model, which is an encoder-decoder model based on inductive graph neural networks designed to rank nodes based on specified CC or BC metrics. We incorporate the MLP-Mixer model as the decoder in the BC ranking prediction task to enhance the model's robustness and capacity. Our approach is evaluated on diverse synthetic and real-world networks of varying scales, and the experimental results demonstrate that the CNCA-IGE model outperforms state-of-the-art baseline models, significantly reducing execution time while improving performance.

Figures (14)

• Figure 1: Degree Centrality's Correlation with Closeness and Betweenness Centrality
• Figure 2: Overview of CNCA-IGE Model. (a) Dataset: Synthetic "Small-World Networks" and "Scale-Free Networks" are employed as training datasets, and "real-world complex networks" are employed as validation datasets. (b) Model Pipeline: Taking the adjacency matrix and the feature matrix (degree) as inductive graph embedding inputs, the embedding vector is obtained after the One-Hot Encoding module, and then the node ranking is obtained through the decoder module. (c) Training Stage: The loss function is constructed based on the actual node rankings and the predicted node rankings to train the model.
• Figure 3: Architectural Overview of GraphSAGE
• Figure 4: Architectural Overview of VGAE
• Figure 5: Architectural Overview of MLP-Mixer