  In network theory, a triad census is a method designed to categorize and
enumerate the various types of subgraphs with three nodes and their connecting
edges within a network. Triads serve as fundamental building blocks for
comprehending the structure and dynamics of networks, and the triad census
offers a systematic approach to their classification. Typically, triad counts
are obtained numerically, but lesser-known methods have been developed to
precisely evaluate them without the need for sampling. In our study, we build
upon Moody's matrix approach, presenting general diagrammatic rules that
systematically and intuitively generate closed formulas for the occurrence
numbers of triads in a network.
