Understanding Edge Connectivity in the Internet through Core Decomposition

The Internet is a complex network composed of several networks: the autonomous systems. Each of them is designed with the aim of transporting information efficiently. This information is carried over routes, which are discovered by routing protocols, such as the border gateway protocol (BGP). The protocols may find possible paths between nodes whenever they exist, or even find paths satisfying specific constraints, e.g., a certain quality of service (QoS). Here, we study connectivity as a network attribute related to both situations; we provide a formal lower bound to it based on core decomposition and low-complexity algorithms to find it. Then we apply these algorithms to analyze maps obtained from the prominent Internet mapping projects, and use the LaNet-vi open-source software for their visualization.