> Is there a standard procedure to
> define fuzzy generalizations of
> typical graph properties?

Consider the concept of a *fuzzy clique*. Define the *cliqueness* $c(G)$ of a graph $G$ as the ratio $\text{deg}(G)\ /\ (|V(G)|-1)$ between the mean degree of $G$ and the number of its vertices (minus one). 

Alternatively: $c(G) = 2\ |E|\ /\ (|V|^2 - |V|)$. 

That is, a graph deviates from being a "true" clique with the number of its missing possible edges. But shouldn't the missing edges been distributed as uniformly as possible among the vertices? Isn't **3** more of a (fuzzy) clique than **2** (which is more of a "true" clique plus an extra vertex), even though they have the same *cliqueness*?

    ![alt text][1][(source)][2]

Should one try to capture this (felt) difference between **2** and **3**? E.g. by considering higher moments of the distribution of missing edges? 

> Is this program (including higher moments) executed somewhere?
> And how is it to be generalized?


  [1]: https://i.sstatic.net/cyWzx.png
  [2]: http://epublius.de/mathoverflow/fuzzy4.png