Triad count estimation in digraphs

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