[Paper Review] Scalable Graph Neural Network-based framework for identifying critical nodes and links in Complex Networks

Sai Munikoti, Laya Das+1 more|arXiv (Cornell University)|Dec 26, 2020

Complex Network Analysis TechniquesPhysics and Astronomy46 references68 citations

TL;DR

This paper proposes an inductive Graph Neural Network (GNN)-based framework, ILGR, to efficiently identify critical nodes and links in large complex networks by learning criticality scores from a small subset of nodes/links. The model achieves over 90% Top-5% identification accuracy and is multiple orders of magnitude faster than conventional iterative methods, enabling scalable and generic robustness analysis across synthetic and real-world networks.

ABSTRACT

Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in the literature on the identification of critical nodes/links are based on an iterative approach that explores each node/link of a graph at a time, repeating for all nodes/links in the graph. Such methods suffer from high computational complexity and the resulting analysis is also network-specific. To overcome these challenges, this article proposes a scalable and generic graph neural network (GNN) based framework for identifying critical nodes/links in large complex networks. The proposed framework defines a GNN based model that learns the node/link criticality score on a small representative subset of nodes/links. An appropriately trained model can be employed to predict the scores of unseen nodes/links in large graphs and consequently identify the most critical ones. The scalability of the framework is demonstrated through prediction of nodes/links scores in large scale synthetic and real-world networks. The proposed approach is fairly accurate in approximating the criticality scores and offers a significant computational advantage over conventional approaches.

Motivation & Objective

• Address the high computational complexity of existing iterative methods for identifying critical nodes/links in large graphs.
• Develop a generic, scalable framework that generalizes across diverse network types and robustness metrics.
• Enable fast, inductive prediction of criticality scores for unseen nodes/links using a trained GNN model.
• Reduce execution time while maintaining high accuracy in critical node/link identification for real-world and synthetic networks.
• Support dynamic network analysis by enabling efficient re-prediction without retraining from scratch upon structural changes.

Proposed method

• Train an end-to-end GNN model on synthetic graphs to learn node and link embedding representations from local sub-graph neighborhoods.
• Use a regression head on node/link embeddings to predict criticality scores based on two robustness metrics: effective graph resistance (Rg) and weighted spectrum (Ws).
• Train the model on a small, representative subset of nodes/links to enable inductive transfer to unseen nodes/links in larger graphs.
• For links, generate link embeddings by combining the embeddings of the two connected nodes using a learnable aggregation layer.
• Employ a two-stage framework: (1) offline training on synthetic data, (2) online inference for unseen graphs with minimal latency.
• Leverage inductive bias from GNNs to generalize across network types and sizes without retraining.

Experimental results

Research questions

• RQ1 Can a GNN-based inductive model achieve high accuracy in predicting critical nodes/links across diverse network types with minimal training data?
• RQ2 How does the proposed GNN framework compare in speed and accuracy to conventional iterative methods that compute criticality scores one node/link at a time?
• RQ3 To what extent does the model generalize to real-world networks it has not seen during training?
• RQ4 Does incorporating link-level embeddings (from node pairs) improve identification accuracy compared to node-only prediction?
• RQ5 How does model performance scale with increasing graph size and complexity?

Key findings

• The ILGR framework achieves a Top-5% identification accuracy of 91% for Rg and 94% for Ws on PL synthetic graphs, and 97.5% for Rg and 96.1% for Ws on PLC synthetic graphs.
• On real-world networks, the model maintains high accuracy: 92.6% (Rg-plc) and 95.2% (ws-plc) for bio-yeast, 93.1% (Rg-plc) and 94.6% (ws-plc) for US Powergrid, and 89.6% (Rg-plc) and 92.5% (ws-plc) for Wiki-Vote.
• The proposed method reduces execution time from over 64,000 seconds (conventional) to under 25 seconds on large graphs like Wiki-Vote, achieving a speedup of multiple orders of magnitude.
• The model generalizes effectively to real-world networks without fine-tuning, demonstrating strong inductive bias and transferability.
• Link identification performance slightly exceeds node identification due to richer link embeddings derived from paired node representations.
• The framework is computationally efficient and scalable, with training time significantly lower than conventional methods, and inference time remains low even for graphs with up to 50,000 nodes and links.