Modelling and Study of t , Peak and Effective Diameter in Temporal Networks

Abstract

Understanding how information, diseases, or influence spread across networks is a fundamental challenge in complex systems. While network diameter has been extensively studied in static networks, its definition and behavior in temporal networks remain underexplored due to their dynamic nature. In this study, we present a formal mathematical framework for analyzing diameter in temporal networks and introduce three time-aware metrics: Effective Diameter , Peak Diameter (*D), and t-Diameter (tD), each capturing distinct temporal aspects of connectivity and diffusion. Our approach combines theoretical analysis with empirical validation using four real-world datasets: high school, hospital, conference, and workplace contact networks. We simulate flow propagation on temporal networks and compare the observed diameters with the proposed theoretical Equations. Across all datasets, our model demonstrates high accuracy, with low RMSE and absolute error values. Furthermore, we observe that the effective diameter decreases with increasing average degree and increases with network size. The results also show that tD and *D are more sensitive to node removal, highlighting their relevance for applications such as epidemic modeling. By bridging formal modeling and empirical data, our framework offers new insights into the temporal dynamics of networked systems and provides tools for assessing robustness, controlling information spread, and optimizing interventions in time-sensitive environments.