A Multi-Dimensional Node Importance Evaluation Method Based on Graph Convolutional Networks

This paper addresses the problem of identifying, evaluating, and ranking key nodes in complex networks by introducing a novel Multi-Parameter Control Graph Convolutional Network (MPC-GCN) for assessing node importance. Drawing inspiration from the multidimensional and hierarchical interactions between nodes in physical systems, this approach integrates the automatic feature learning capabilities of Graph Convolutional Networks (GCNs) with a comprehensive analysis of nodes’ intrinsic properties, their interactions with neighbors, and their roles within the broader network. The MPC-GCN model offers an innovative framework for key node identification, leveraging GCNs to iteratively aggregate node and neighbor features across layers. This process captures and combines local, global, and positional characteristics, enabling a more nuanced, multidimensional assessment of node importance. Moreover, the model incorporates a flexible parameter adjustment mechanism, allowing the relative weights of different dimensions to be tuned, thereby adapting the evaluation process to various network structures. To validate the model’s effectiveness, we first tested the influence of model parameters on randomly generated small networks. We then conducted extensive simulations on eight large-scale networks using the Susceptible-Infected-Recovered (SIR) model. Evaluation metrics, including the M(R) score, Kendall’s tau correlation, the proportion of infected nodes, and the relative size of the largest connected component, were used to assess the model’s performance. The results demonstrate that MPC-GCN outperforms existing methods in terms of monotonicity, accuracy, applicability, and robustness, providing more precise differentiation of node importance. By addressing the limitations of current methods—such as their reliance on single-dimensional perspectives and lack of adaptability—MPC-GCN offers a more comprehensive and flexible approach to node importance evaluation. This method significantly improves the breadth and applicability of node ranking in complex networks.