ENTROPY - RESISTANCE BASED TOPOLOGICAL INDEX FOR DYNAMIC NETWORK COMPLEXITY AND INFORMATION FLOW ANALYSIS

Abstract

Dynamic networks offer numerous advantages for communication and computing processes, particularly due to the constant changes in their topology. Traditionally, measuring network complexity has relied on either entropy measures or resistance distance measures independently. This highlights the need for a combined approach that incorporates both measures for a comprehensive assessment of network complexity in dynamic networks.  In this paper, we introduce the Entropy Resistance Index (ERI) as a new metric for measuring network complexity in dynamic settings. We mathematically formulated this proposed metric and conducted simulations using dynamic graph models, including random, scale-free and small-world graphs. These simulations accounted for changing factors such as node failures, edge perturbations and variations in traffic. The results showed that the ERI metric yielded better outcomes compared to classical methods, which relied solely on entropy or resistance metrics. Specifically, the model for the ERI metric achieved a complexity sensitivity value of 0.91, a diffusion efficiency of 0.93, a robustness factor of 0.90 and a stability rating of 0.92 - all of which were superior to those observed in classical approaches. Furthermore, the ERI values effectively detected variations in network topologies and communication patterns. Finally, theoretical proof demonstrated that the proposed metric is always positive, bounded, stable and sensitive to connectivity changes.