  Given a finite set T of maps on a finite ring R, we look at the finite simple
graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T,
b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite
set of quadratic maps T_i(x)=x^2+a_i. Graphs defined like that have a
surprisingly rich structure. This holds especially in an algebraic set-up when
T is generated by polynomials on Z_n. The characteristic path length L and the
mean clustering coefficient C are interlinked by global-local quantity
LC=-L/log(C) which often appears to have a limit for n to infinity like for two
quadratic maps on a finite field Z_p. We see that for one quadratic map x^2+a,
the probability to have connectedness goes to zero and for two quadratic maps,
the probability goes to 1, for three different quadratic maps x^2+a,x^2+b,x^2+c
on Z_p, we always appear to get a connected graph for all primes.
