Triadiset

Triadiset is a term used in graph theory and network analysis to denote a collection of triads, that is, subgraphs formed by three vertices and the edges among them, drawn from a larger network for study. A triadiset acts as a dataset or building block for examining local network structure and for motif analysis.

In practice, a triadiset records, for each triad, which of the possible edges among the three nodes are present and may include additional attributes such as edge weights, directions, or node labels. In undirected graphs, triads fall into four isomorphism classes: the null triad (no edges), the single-edge triad, the two-edge triad (a path of length two), and the triangle (three edges). Directed graphs admit a larger taxonomy of triads based on edge orientation.

Construction and use: Triadsets can be created by enumerating all 3-node combinations or by sampling from the network. They may be weighted, with weights reflecting edge strengths or frequencies, and can be used to compute triad-based statistics such as triad density, closure, and motif significance compared to null models.

Relation to related concepts: Triad census, network motifs, and subgraph mining often use triad datasets as a basis for analysis. The term triadiset is not universally standardized and may be defined differently across studies.