Triad count estimation in digraphs

One may use information about a random sample of network members to estimate quantities related to the triad census of a network. Various kinds of information about the graph may be observable from the sample; four observation schemes involving the local networks of the sampled vertices are considered here. Unbiased triad count estimators are defined, and their variances (and unbiased estimators of these variances) are derived. A main result is that under one of the observation schemes, the estimator can be written as a sum of vertex attributes; standard estimation formulas for various sampling designs, such as stratified sampling, are therefore effortlessly applied. The estimator properties are compared in a simulation study.