A k-regular simple graph G on ν nodes is strongly k-regular if there exist positive integers k, λ, and μ such that every vertex has k neighbors (i.e., the graph is a regular graph), every adjacent pair of vertices has λ common neighbors, and every nonadjacent pair has μ common neighbors. A graph that is not strongly regular is said to be weakly regular. A distance-regular graph with graph diameter d = 2 is a strongly regular graph. Strongly regular graphs are therefore distance-regular. Connected strongly regular graphs are conformally rigid.
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