The situation is considered whether a graph can be assumed to have been generated by a random model capturing more transitivity than a simple uniform model. Three different test quantities based on induced triad counts and local densities are used. A simulation study is made in order to estimate critical values of the tests for different significance levels. The powers of the tests are estimated against the Bernoulli triangle model, a simple random graph model in which the clustering and transitivity is higher than in the uniform model. The test based on the proportion of transitive triads has the highest power in most cases, but the test based on density difference (the difference between mean local density and overall graph density) is more powerful against models with high transitivity. The tests are applied to a large set of school class sociograms. In this situation, uniform randomness is rejected in favor of transitivity most frequently when the test based on the proportion of transitive triads out of the non-vacuously transitive triads is used. It is concluded that this test, which also performed reasonably well when applied to random data, is the best at detecting transitivity. Although the Bernoulli triangle model fits to the empirical data set better than the uniform model, there are fewer truly intransitive triads in the data than could be expected under either of the models. (C) 1997 Elsevier Science B.V.
