This work focuses on the problem of dynamic centrality, a measure of node importance in time-dependent networks, and addresses how to steer network centrality to a desired state by making minimal modifications to the network structure.
Abstract
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.
This paper studies the problem of steering collective beliefs in social networks when only a small fraction of nodes can be directly influenced. We propose a sparse optimal control framework built on the Network Drift-Diffusion Model (NDDM). Two intervention mechanisms are considered: direct control and latent (indirect) control. To select which nodes to actuate, we compare six centrality measures---Degree, Betweenness, Eigenvector, Closeness, PageRank, and K-shell---and keep only the top 5\%--30\% as control inputs. The optimal feedback law follows from the Hamilton-Jacobi-Bellman (HJB) equation, which reduces to solving Riccati-type differential equations. We test our approach on Erdős-Rényi (ER), Barabási-Albert (BA), and Watts-Strogatz (WS) networks. The results show that the best centrality choice depends strongly on the network topology, and the system undergoes phase transitions as control parameters vary.
Bo Wang· Frontiers in Computing and I...· 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.
Network theory has great significance in the assessment of complex systems in various domains such as computer science, biology, social sciences, and communication systems. This research paper provides a detailed discussion of network theory through the application of graph theory methods to assess networks and analyse interconnected systems. Graph theory is a branch of mathematics in which nodes represent entities and edges represent the relationships between them. Various aspects of graph theory, such as graph representation, connectivity, centrality measures, clustering behavior, and shortest path algorithms, are discussed to assess network performance. Additionally, popular network models, including random, small-world, and scale-free networks, are discussed. The practical applications of network theory in several domains, such as social networks, transportation systems, biological networks, and communication systems, are also covered in this research paper. Experimental analysis on benchmark datasets proves that the use of a graph-theoretic approach enhances the efficiency of the network analysis process and simplifies the identification of influential nodes within a network.
D. M· Recent Research Reviews Jour...· 0 citations
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.
A. Kurudi̇rek, Ibrahim Filik, Sravan Sakhamuri et al.· 2026 International Conferenc...· 0 citations
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.
Shilun Zhang, A. Ceria, Hui-Juan Wang· Communications Physics· 0 citations
Spectral Efficiency Centrality (SEC), a temporal spectral centrality framework that quantifies node importance by evaluating the change in spectral radius caused by node removal across temporal snapshots, and ASEC, an efficient approximation based on Perron-Frobenius theory and first-order eigenvalue perturbation that offers a computationally efficient solution for large-scale temporal networks.
Aksa Urooj, Iqra Altaf Gillani· 0 citations
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