The Iterated Local Directed Transitivity Model

 We present a new, deterministic directed graph model for social networks, based on the transitivity of triads. In the Iterated Local Directed Transitivity (ILDT) model, new vertices are born over discrete time-steps and inherit the link structure of their parent vertices. The ILDT model may be viewed as a directed graph analog of the Iterated Local Transitivity model for undirected graphs. We also investigate the theoretical properties of ILDT digraphs. We prove that the ILDT model exhibits a densification power law, so that the digraphs generated by the models densify over time. The number of directed triads are investigated, and counts are given of the number of directed 3-cycles and transitive 3-cycles. A higher number of transitive 3-cycles are generated by the ILDT model, as found in realworld, on-line social networks that have orientations on their edges. We discuss the eigenvalues of the adjacency matrices of ILDT digraphs.