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

TL;DR

This paper introduces a formal framework and new metrics for analyzing the diameter of temporal networks, validated with real-world data, revealing insights into their dynamic connectivity and implications for spreading processes.

Contribution

It presents a novel mathematical framework and three time-aware diameter metrics for temporal networks, validated with empirical data, enhancing understanding of their dynamic properties.

Findings

Effective diameter decreases with higher average degree.

t-Diameter and Peak Diameter are sensitive to node removal.

Model accurately predicts diameters with low error across datasets.

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.