It is shown, for the Susceptible-Infectious threshold process on temporal higher-order networks derived from human face-to-face interactions, that the contribution of each hyperlink can be quantified by a contagion backbone, whose dependency on the diffusion parameters is demonstrated and supported by theoretical analysis.
Abstract
Temporal higher-order networks, where each hyperlink involving a group of nodes is activated or deactivated over time, effectively represent social interactions. They serve as substrates for the spread of epidemics and information. However, the contribution of each hyperlink to a contagion process, namely, the average number of nodes that are infected via its activation, and the network properties of hyperlinks that influence this contribution, remain unexplored. Here we show, for the Susceptible-Infectious threshold process on temporal higher-order networks derived from human face-to-face interactions, that the contribution of each hyperlink can be quantified by a contagion backbone, whose dependency on the diffusion parameters is demonstrated and supported by theoretical analysis. We design centrality metrics of hyperlinks to estimate hyperlink rankings based on their contributions, revealing that local properties of hyperlinks can effectively identify high-contributing hyperlinks, and explain why different centrality metrics perform better under different process parameters. These insights are crucial for designing effective interventions that mitigate the spread of epidemics or misinformation.
This work proposes a community-based preferential attachment hypergraph model with tunable modularity and a heavy-tailed degree distribution, reproducing key structural properties in real systems, and develops a hypergraph-based SAIR framework to describe epidemic dynamics with asymptomatic transmission.
Network epidemic simulation enables fine-grained understanding of epidemic behavior. However, empirical samples of interaction networks display properties that are challenging to capture with popular synthetic models of networks. Our empirical results show that epidemic spread behavior is sensitive to a form of multi-scale local structure that is absent in common baseline models, (e.g., Erdős–Rényi, Chung-Lu, etc). This structure critically impacts the effect of local quarantining and stops epidemic spread in samples of interaction networks, even when it cannot be halted in simple synthetic models of those networks. Insights from our analysis include how epidemics on networks with widespread multi-scale local structure are easier to mitigate, as well as characterizing which nodes are ultimately not likely to be infected. We demonstrate that this structure results from more than just local triangle structure in the network, and we illustrate processes based on homophily or social influence and random walks that suggest how this multi-scale local structure arises and use it to cleanly isolate intervention sensitivity to multi-scale local structure.
Omar Eldaghar, Michael W. Mahoney, D. Gleich· PLOS Complex Systems· 0 citations
This work investigates the susceptible-infected-susceptible epidemic model on clustered regular networks using the pair mean-field approach, where higher-order effects are explicitly considered in dynamic analysis and proves the effectiveness of the pair mean-field method for analyzing higher-order network dynamics.
Qing-Chu Wu, Zhao-Yan Wu· Journal of Mathematical Biol...· 0 citations
Temporal networks offer a suitable representation for complex systems in which interactions vary over time, such as communication, transportation, and social networks. Identifying influential nodes in such networks is more challenging than in static graphs because node importance depends not only on network structure but also on the timing and ordering of interactions. Although many temporal centrality measures have been proposed, the literature remains fragmented, with limited consensus on their comparative performance and applicability. This paper presents a critical and comparative survey of centrality measures in temporal networks. We review both temporal extensions of classical centrality metrics and measures specifically designed for temporal graphs, and propose a functional taxonomy that categorizes existing approaches according to the primary mechanism through which influence is quantified in temporal networks. The proposed taxonomy organizes temporal centrality measures into interaction-based, path-based, walk-based, spectral-based and robustness-based categories, providing a unified perspective on their underlying principles. In addition, we provide comparative insights to help select appropriate temporal centrality measures under different network characteristics and application settings. To complement the survey, we conduct experiments on multiple real-world temporal network datasets. The measures are evaluated through influence spreading experiments using epidemic diffusion models, ranking consistency analysis based on Kendall's rank correlation, and runtime complexity analysis to assess computational efficiency and scalability. Finally, we highlight key open challenges and future research directions, including scalability for million-sized networks and the need for standardized evaluation frameworks.
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
Time-evolving networks, or temporal networks, play a crucial role in modeling dynamic interactions across various domains, including biology, social sciences, and information technology. Unlike static networks, these systems undergo continuous changes in topology and edge weights, influencing processes such as information flow, transportation efficiency, and neural activity. Understanding and controlling these networks are essential for predicting future behavior and optimizing dynamic processes. This work focuses on the problem of dynamic centrality, a measure of node importance in time-dependent networks. Specifically, we address how to steer network centrality to a desired state by making minimal modifications to the network structure. This problem is formulated as an optimal control problem for an ordinary differential equation, either matrix- or vector-based, where the control acts on network edges. The proposed framework generalizes centrality control problems studied in static networks and leverages the Pontryagin Maximum Principle for efficient solutions. For large-scale problems, the required matrix-function actions are approximated by Krylov-type techniques, avoiding the explicit formation of dense matrix functions. Numerical experiments on synthetic and real temporal networks show that the proposed framework can effectively steer receive centrality under prescribed control constraints.
