Experimental results for two-dimensional grain growth are compared with the results obtained from computer-generated random threefold vertex networks with a fixed one-particle distribution function. A considerable discrepancy in the two-particle distributions implies some kind of short-range order. New results in the computer simulation of normal grain growth are reported, demonstrating a similar kind of ordering. A simple relation is suggested for the quantitymn, introduced by Aboav and the second moment of the one-particle distribution μ2