Key physical topology features for optical backbone networks via a multilayer correlation analysis

Abstract

A communication network is a multilayer network comprising various layered technologies, and the underlying physical topology is an important aspect that determines the upper bound of overall system performance, including total communication capacity, cost, and robustness. We expect that understanding the impact of the physical topology on system performance will lead to better optical communication network design in the future, and we thus focus on clarifying the relationship between physical topology features and system performance. There have been various studies on the relationship between topology features and overall network performance. For example, the average number of hops and the cluster coefficient are well known to change network properties in complex networks. From the perspective of optical communication networks, it is known that the algebraic connectivity and average path length are related to total network capacity, and these findings have been applied in physical topology design models. On the other hand, there have been no quantitative comparisons among various topology features, and the comprehensiveness of the population from which these features are extracted is insufficient. Hence, we have developed a multilayer (physical topology and layer 1) correlation analysis framework that enables a quantitative comparison of topology features. We use this framework to numerically examine the relationships between physical topology features and the total communication capacity, cost, and robustness of optical communication networks, including graph features (especially graph spectra) that have not been investigated. The results show that the Laplacian spectral radius and geodesic distance Laplacian spectral radius are strongly related to system performance, in addition to the conventional average number of hops, cluster coefficient, algebraic connectivity, and average path length. We confirm that these correlations hold for the different network sizes and spatial nonuniformity of real optical backbone networks in different countries and regions. The results show that the average path length and cluster coefficient, or the Laplacian spectral radius and geodesic distance Laplacian spectral radius, are important guidelines for physical topology design of real optical backbone networks.