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. The complete graph K_n is strongly regular for all n>2. The status of the trivial singleton graph K_1 is unclear. Opinions differ on if K_2 is a strongly regular graph, though since it has no well-defined μ parameter, it is preferable to consider it not to be strongly regular (A. E. Brouwer, pers. comm., Feb. 6, 2013).
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