A communication arc from A to B represents the transmission of a single message from the first system A to the second system B. What are all the ingredients of a communication arc required for the sending of a message? What compatibility conditions between these two systems must be satisfied in order for communication to take place? Further, what does each ingredient comprise and just when do these compatibility conditions work? Answers to these questions are sought through the use of the natural theoretical framework provided by graph theory. Although the discussion is restricted to a communication model, its applications extend to all real-world situations involving networks. The object of the investigation is to delineate the anatomy of a communication arc in sufficient careful detail that an arc can be recognized, synthesized, and analyzed. (For related documents, see ED 056 256, 257, and 259.) (Author)