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The Iterated Local Directed Transitivity Model for Social Networks
- Publication Year :
- 2019
-
Abstract
- 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 \cite{ilt}. We investigate network science and graph 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 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.
- Subjects :
- Computer Science - Social and Information Networks
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1912.08924
- Document Type :
- Working Paper