The Iterated Local Directed Transitivity Model for Social Networks [article]

Anthony Bonato and Daniel W. Cranston and Melissa Huggan and Trent Marbach and Raja Mutharasan
2020 arXiv   pre-print
We introduce a new directed graph model for social networks, based on the transitivity of triads. In the Iterated Local Directed Transitivity (ILDT) model, new nodes are born over discrete time-steps, and inherit the link structure of their parent nodes. The ILDT model may be viewed as a directed analogue of the ILT model for undirected graphs introduced in . We investigate network science and graph theoretical properties of ILDT digraphs. We prove that the ILDT model exhibits a densification
more » ... wer 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 real-world, on-line social networks. In many instances of the chosen initial digraph, the model eventually generates graphs with Hamiltonian directed cycles. We finish with a discussion of the eigenvalues of the adjacency matrices of ILDT directed graphs, and provide further directions.
arXiv:1912.08924v3 fatcat:cebwmhz3q5crbnwn2ofuuknjwi