Before revision:  In this paper we consider a localized version of the classical notion of clique number for the aforementioned ER-perturbed random geometric graphs : Specifically, we study the edge clique number for each edge in a graph, defined as the size of the largest clique(s) in the graph containing that edge.
After revision:  In this paper we consider a localized version of the classical notion of clique number for the aforementioned ER-perturbed random geometric graphs : Specifically, we study the edge clique number for each edge in a graph, defined as the size of the largest clique(s) in the graph containing that edge.