  We show that the random number $T_n$ of triangles in a random graph on $n$
vertices, with a strict constraint on the total number of edges, admits an
expansion $T_n = an^3 + bn^2 + F_n$, where $a$ and $b$ are numbers, with the
mean $\langle F_n \rangle = O(n)$ and the standard deviation $\sigma(T_n)
=\sigma(F_n)= O(n^{3/2})$. The presence of a `surface term' $bn^2$ has a
significance analogous to the macroscopic surface effects of materials, and is
missing in the model where the edge constraint is removed. We also find the
surface effect in other graph models using similar edge constraints.
