Measuring tendency towards mutuality in a social network

When trying to understand the structure of a social network, the number of mutual dyads is often used to describe tendency toward mutuality (TTM). Only few works, however, deal with measures of TTM and only the work of Rao and Bandyopadhyay [Rao, A.R., Bandyopadhyay, S., 1987. Sankhya 49 Ser. A, pp. 141-188] compares between the different measures. This paper presents the different measures for TTM, their interpretation and their advantages and disadvantages. We also explore the distribution of the number of mutual dyads in graphs which are distributed according to a uniform distribution over certain special spaces. The measures are demonstrated and compared on two independent real data sets.