digraphs

Digraphs is a term with two common meanings in different fields. In linguistics and orthography, a digraph is a pair of letters that together represent a single sound or a single phoneme. In English and many other languages, digraphs include combinations such as ph (representing /f/), ch (often /tʃ/), sh (/ʃ/), th (/θ/ or /ð/), and ng (/ŋ/). Digraphs can also produce sound values that are not obvious from either letter alone, and some two-letter sequences are not digraphs in a given language. The concept is a useful way to describe how writing systems encode speech, and distinctions between phonemes and graphemes can vary by language and analysis. Digraphs are sometimes contrasted with trigraphs, which use three letters to represent a single sound, and with monographs, which are single letters.

In graph theory, a digraph, short for directed graph, is a set of vertices connected by directed edges. An edge in a digraph has an orientation, going from a source vertex to a destination vertex. Digraphs may be simple, allowing at most one arc from u to v and usually disallowing loops; they may also permit loops (edges from a vertex to itself) and multiple edges between the same pair of vertices. Key concepts include in-degree and out-degree of vertices, directed paths and directed cycles, and notions of reachability and strong connectivity. The adjacency matrix of a digraph records whether an arc exists from one vertex to another.

Applications of digraphs appear across disciplines. In computer science, they model state machines and data flow; in operations research they represent precedence constraints and network flows; in biology they can describe metabolic or protein interaction networks. In linguistics, the term digraph helps describe how writing systems encode sounds.