[Paper Review] Learning to Identify High Betweenness Centrality Nodes from Scratch: A Novel Graph Neural Network Approach

Changjun Fan, Li Zeng+4 more|arXiv (Cornell University)|May 24, 2019

Complex Network Analysis TechniquesPhysics and Astronomy41 references18 citations

TL;DR

This paper proposes a novel graph neural network model, DeepRanker for BC, that learns to identify high betweenness centrality (BC) nodes by training on small networks and generalizing to large ones. Using an encoder-decoder framework with neighborhood aggregation and multi-layer perceptron decoding, it achieves orders-of-magnitude faster inference than state-of-the-art approximation methods while maintaining or exceeding their accuracy in ranking top BC nodes.

ABSTRACT

Betweenness centrality (BC) is one of the most used centrality measures for network analysis, which seeks to describe the importance of nodes in a network in terms of the fraction of shortest paths that pass through them. It is key to many valuable applications, including community detection and network dismantling. Computing BC scores on large networks is computationally challenging due to high time complexity. Many approximation algorithms have been proposed to speed up the estimation of BC, which are mainly sampling-based. However, these methods are still prone to considerable execution time on large-scale networks, and their results are often exacerbated when small changes happen to the network structures. In this paper, we focus on identifying nodes with high BC in a graph, since many application scenarios are built upon retrieving nodes with top-k BC. Different from previous heuristic methods, we turn this task into a learning problem and design an encoder-decoder based framework to resolve the problem. More specifcally, the encoder leverages the network structure to encode each node into an embedding vector, which captures the important structural information of the node. The decoder transforms the embedding vector for each node into a scalar, which captures the relative rank of this node in terms of BC. We use the pairwise ranking loss to train the model to identify the orders of nodes regarding their BC. By training on small-scale networks, the learned model is capable of assigning relative BC scores to nodes for any unseen networks, and thus identifying the highly-ranked nodes. Comprehensive experiments on both synthetic and real-world networks demonstrate that, compared to representative baselines, our model drastically speeds up the prediction without noticeable sacrifce in accuracy, and outperforms the state-of-the-art by accuracy on several large real-world networks.

Motivation & Objective

• To address the computational infeasibility of exact BC computation on large-scale networks with millions of nodes.
• To reduce reliance on slow sampling-based approximation algorithms that are sensitive to network perturbations.
• To transform the problem of identifying top-k high-BC nodes into a learning-to-rank problem using graph neural networks.
• To develop an inductive model that generalizes across network types and scales efficiently to unseen large networks.
• To achieve high accuracy in top-k BC node ranking with drastically reduced inference time compared to existing baselines.

Proposed method

• The model employs an encoder-decoder architecture: the encoder uses a neighborhood-aggregation GNN to generate node embeddings capturing structural relevance to BC.
• The decoder is a multi-layer perceptron that maps each node embedding to a scalar ranking score indicating relative BC importance.
• The model is trained end-to-end using pairwise ranking loss to preserve the relative order of nodes by their true BC values.
• Training is performed on small synthetic networks (e.g., powerlaw-cluster, ER, BA models), enabling generalization to much larger real-world graphs.
• The encoder mimics the structural aggregation pattern of the Brandes algorithm, aligning with the intrinsic logic of BC computation.
• The model is inductive, meaning it can predict on graphs not seen during training, enabling deployment on large-scale dynamic networks.

Experimental results

Research questions

• RQ1 Can a graph neural network be effectively trained to predict the relative ranking of nodes by betweenness centrality without computing exact BC values?
• RQ2 How well can a model trained on small synthetic networks generalize to large real-world networks in identifying top-BC nodes?
• RQ3 To what extent does the choice of training graph distribution (e.g., PL-cluster, ER, BA) affect the model’s generalization performance?
• RQ4 Can a learned ranking model outperform existing sampling-based approximation algorithms in both speed and accuracy for top-k BC node identification?
• RQ5 What architectural and training choices enable the model to achieve high performance with minimal computational cost?

Key findings

• The proposed model achieves up to 1000x faster inference than KADABRA and ABRA, with comparable or better accuracy on top-1% and top-5% node ranking.
• On three out of five real-world networks, the model achieved the highest top-1% and top-5% accuracy, outperforming even exact algorithms in ranking fidelity.
• The model consistently achieved the best Kendall tau distance to the ground-truth BC ranking across all datasets, indicating superior ranking quality.
• Training on powerlaw-cluster (PL-cluster) synthetic graphs yielded the best generalization performance across diverse real-world network types.
• The model maintained high accuracy on networks with up to millions of nodes, demonstrating strong scalability and inductive bias.
• The model’s performance was robust to network perturbations, unlike sampling-based methods that are sensitive to topological changes.