I have a network of N sensors and a test that tells me whether two sensor outputs are definitely *not* causally related. This allows me to construct a causality graph where each sensor is a vertex and two vertices share an edge if they have passed the test.

Naturally, I'm looking for large cliques to see if the sensor network got anything of note. Causality graphs for one of the event types that I observe have an interesting property: they have one big clique and a set of vertices that are adjacent to the clique, but not each other. Like nodes 4 and 5 here:

Is there an optimal way to count these vertices? Right now I simply look for one-element subtractions of large cliques, but there is probably a body of work on the subject.

More generally, what kind of graph property am I dealing with and what terminology should I look up?