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 , 7, ... nodes are 2, 4, 16, 21, ... (OEIS A076434).

The following table lists some named weakly regular graphs. Here, the parameters
give the vertex count , the degree , the possible common neighbors of adjacent vertices , and the possible common neighbors of nonadjacent vertices
.
At least one of the latter two parameters will have two values for a weakly regular
graph (otherwise, the graph would be strongly
regular).