Space Geometry Effect over the Internet as a Physical-Logical Interdependent Network

Abstract

In this article we study the Internet’s robustness under physical node failures, given that the physical layer is built over spaces with geometry/shape restrictions. This is of special interest for countries prone to natural catastrophes, and long and narrow geographies such as Chile and Japan. We model the Internet as an interdependent network composed of the Internet’s physical layer (Internet backbone) and he Internet’s logical layer (Autonomous System level network) coupled. Here, the robustness is tested by measuring the amount of functional nodes on the logical network after randomly removing physical nodes. In this work, we tested six different spatially constrained network models to generate the Internet’s physical layer (Yao graphs, geometric preferential attachment, Erdős-Rényi, n-nearest neighbours, Gabriel graphs, and Modified relative neighbourhood model), and three different geometries with width to lengths ratios going from a square geometry to a Chile-like space geometry. Additionally, we study the relation between the amount of physical edges and the Internet’s robustness. Our findings suggest that both: the edge addition strategy (i.e. the physical network model used) and the amount of physical edges play an important role on the Internet’s robustness. Our results also suggest that Internet based interdependent systems whose robustness is affected by the space geometry (geometry-sensitive) can become more robust by randomly adding few edges. Furthermore, these interdependent systems can become geometry-insensitive after the edge addition, meaning that the robustness of the interdependent system is no longer affected by the space geometry.