Transitivity in stochastic graphs and digraphs

Transitivity is a central concept for many relational structures, e.g. clusterings and partial orderings. Stochastic graph models which are used to describe uncertain relational structures can be tested for transitivity by using indices based on triad counts. The pure random variation of such counts and indices is investigated assuming simple stochastic models. Some earlier results on transitive triads in tournaments are generalized, and a modified version of a randomization model by Holland and Leinhardt which simplifies the required moment calculations is introduced.