A weakly regular graph is a regular graph that is not strongly regular. Under the convention
used here, 
is weakly regular and is the only such simple graph
on fewer than six nodes. The numbers of nonisomorphic
weakly regular graphs on 
, 7, ... nodes are 2, 4,
16, 21, ... (OEIS A076434, restricted here
to 
).
The following table lists some named weakly regular graphs. Here, the parameters 
give the vertex count 
, the degree 
, the possible numbers 
of common neighbors of adjacent
vertices, and the possible numbers 
of common neighbors of nonadjacent vertices. Except for 
, at least one of the latter two parameters
takes two or more distinct values for a weakly regular graph (otherwise, the graph
would be strongly regular).
graph
