Methodology to quantify robustness in networks: case study—Higher Education System in Mexico

In this work, we propose a methodology to quantify robustness in networks. Specifically, the methodology is based on the resolution of the Vertex Separator Problem in order to find the set of nodes that the elimination of their links causes the rupture of the giant component. The methodology presented in this work was tested on a set of benchmark networks and on set of social networks modeled with the information about the main characteristics of the universities belonging to the Higher Education System in Mexico (HESM) for the period 2013–2017. The results show that the proposed methodology is able to quantify the robustness in several types of networks without using centrality measures or some other structural metric. On the other hand, regarding the HESM networks, we can assure that they are robust and that they are prone to generate communities or modules.