Institute for Mathematical Behavioral Sciences

The Pólya enumeration theorem (PET) is a powerful tool for counting various isomorphism classes. It has been used by Harary and Palmer (1973) to count the number of graphs and digraphs. In the present study, we extend these results to the enumeration of signed graphs and digraphs. Our goal is to obtain the triad census of a random graph model for social networks. These results are important to determine the variance and covariance of various combinations of triads, as in the structural balance and equivalence models. Using these results, we can establish indices of these models with zero mean and unit standard deviation.