A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n = 6, 7, ... nodes are 2, 4, 16, 21, ... (OEIS A076434). The following table lists some named weakly regular graphs. Here, the parameters (n, k, λ, μ) give the vertex count n, the degree k, the possible common neighbors of adjacent vertices λ, and the possible common neighbors of nonadjacent vertices μ. At least one of the latter two parameters will have two values for a weakly regular graph (otherwise, the graph would be strongly regular).

regular graph | strongly regular graph