The Mayer f-function for purely hard particles of arbitrary shape satisfies f^2(1, 2) = -f(1, 2). This relation can be introduced into the graphical expansion of the direct correlation function c(1, 2) to obtain a graphical expression for the case of exact coincidence, in position and orientation, of two identical hard cores. The resulting expression for e(1, 1)+ 1 contains only graphs G from c(1), the sum of irreducible graphs with one labeled point. Relative to its coefficient in c(1), G occurs in c(1, 1) with an additional factor Re, which is 1 for the leading graph in the expansion and of the form 2-2L(G) for all other graphs. Here L(G) = 0, 1, 2 ..... is a nonnegative integer. Topological analysis is used to derive an expression for L(G) in terms of the connectivity properties of G.