Aug 2026· International Journal of Modern Physics C· 0 citations
TL;DR
A model for identifying influence nodes in multilayer networks that leverages multilayer feature fusion, encompassing intra-layer features, weighted centrality features, and inter-layer structural features is proposed, which outperforms classical and heuristic baselines in terms of resilience, generalization, and robustness.
Abstract
Multilayer networks offer a powerful framework for modeling complex systems in which nodes engage in multiple types of interactions across interconnected layers. The Identification of influential nodes in multilayer networks is a growing research problem and is relatively less explored. There are numerous studies that have addressed influential node identification in single-layer networks, but very few have focused on multilayer networks. Moreover, existing methods for identifying influential nodes in multilayer complex networks often overlook the complex inter-layer coupling or rely on simple linear heuristics that fail to capture the intricate, non-linear relationship between network topology and spreading dynamics. This paper proposes a model for identifying influence nodes in multilayer networks that leverages multilayer feature fusion, encompassing intra-layer features, weighted centrality features, and inter-layer structural features. The ground truth for learning is obtained through a multilayer Susceptible–Infected–Recovered (SIR) simulation, where infection probabilities are dynamically determined from layer-specific degree distributions, allowing for the realistic modeling of heterogeneous diffusion dynamics. An XGBoost-based ensemble regression model is then trained to learn the non-linear mapping between node-level features and their diffusion-based influence. Furthermore, experiments on nine real-world multilayer datasets demonstrate that the proposed model outperforms classical and heuristic baselines in terms of resilience, generalization, and robustness.
This study introduces a new ranking framework that integrates a quasi-Laplacian structural measure with a gravity-inspired aggregation process and demonstrates that the proposed framework consistently outperforms existing techniques in terms of accuracy, resolution, and computational simplicity.
Accurate identification of key nodes in dynamic temporal networks is critical to network propagation control and governance. To address the issues that traditional temporal multilayer networks insufficiently consider node heterogeneity and inadequate inter-layer information fusion, this paper proposes the MSAM (Supra-Adjacency Matrix based on Multi-order Neighborhood Structure) model for node importance identification based on inter-layer multi-order structure similarity. The model characterizes intra-layer attributes via K-shell decomposition and the Pareto principle, measures inter-layer similarity by integrating multi-order neighbor and hierarchical fluctuation information, and realizes heterogeneous node coupling modeling. Experiments on real-world datasets demonstrate that MSAM achieves significantly better ranking performance than baseline models. It exhibits strong robustness and generalization ability under different propagation intensities, effectively improving the accuracy of node importance identification in dynamic networks.
Network datasets in modern applications often involve multiple types of interactions occurring over a shared set of individuals. Characterizing the generating mechanisms of these interactions can be enhanced by joint modelling, as shared vertices allow layers to help explain the structure of other layers. We model multiplex observations using graph limits, called a scaled set of graphons, and develop a nonparametric joint estimator based on blockmodel approximations, termed the multi-network histogram. This nonparametric framework captures each layer's varying sparsity and connection structure, accounting for heterogeneity via shared latent variables across all layers. We establish the theoretical properties of the multi-network histogram, providing an upper bound for the weighted mean integrated squared error and deriving the optimal bandwidth that minimizes this error. By leveraging information across layers, this joint modelling achieves a reduction in error and a smaller optimal bandwidth, which enables high-resolution estimation even in sparser layers. Its usefulness is demonstrated through simulation studies and an application to socioeconomic networks in an Indian village.
Identifying influential nodes in complex networks is a fundamental problem with applications in information diffusion, epidemic control, infrastructure robustness, and biological systems. Traditional approaches rely on structural centrality measures, such as degree, betweenness, closeness, and PageRank, which quantify node importance based on network connectivity. However, these measures do not explicitly account for diffusion dynamics and the structural impact of node removal, where both spreading capability and network resilience play a critical role. In this paper, we propose a unified framework that jointly captures diffusion-based influence and structural resilience. We first introduce an SIR-based centrality in which node influence is defined by its spreading capability, while resilience is quantified by measuring the change in total network diffusion after node removal. To address the computational cost of this formulation, we propose the Resilient-Influential Node (RIN) centrality, which efficiently approximates the unified objective by combining classical centrality measures with a Laplacian-based structural adjustment. Experimental results on multiple real-world networks, using SIR-based rankings as ground truth, show that the proposed RIN framework provides a consistent and principled characterization of influential and resilient nodes across diverse network structures.
Afra Kurudirek, Ibrahim Filik, Sravan Sakhamuri et al.· 2026 International Conferenc...· 0 citations
WKDH fuses local structural attributes with global structural attributes via a multiplicative weighted synergy model, simultaneously capturing local connection “quantity,” local connection “quality,” and global core-layer position, and achieves linear computational complexity of O(m).
Na Zhao, Chaozhou Dai, Guo-Lin Yang et al.· Entropy· 0 citations
Experimental results in seven complex networks of the real world show that the proposed hybrid centrality called k-core neighborhood density (KND) remarkably balances rank distribution and accuracy, and the identified influential nodes have a superior ability to spread their influence over a wide area of a network.