Regular clique assemblies, configurations, and friendship in Edge-Regular graphs

Source abstract

An edge-regular graph is a regular graph in which, for some $\lambda$, any two adjacent vertices have exactly $\lambda$ common neighbors. This paper is about the existence and structure of edge-regular graphs with $\lambda =1$ and about edge-regular graphs with $\lambda >1$ which have local neighborhood structure analogous to that of the edge-regular graphs with $\lambda =1$.