The Iterated Local Directed Transitivity Model for Social Networks

Bonato, Anthony; Cranston, Daniel W.; Huggan, Melissa A.; Marbach, Trent G.; Mutharasan, Raja

doi:10.1007/978-3-030-48478-1_8

Cited by 10 publications

(5 citation statements)

References 14 publications

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“…For item (2), to show that e t+1 = 3e t + 2n t , we consider how new arcs are added to G t . Every arc (x, y) in G t generates one out-degree from…”

Section: Key Properties Of Complex Networkmentioning

confidence: 99%

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The Iterated Local Directed Transitivity Model

Mutharasan¹

2023

Preprint

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<p> 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. </p>

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“…For item (2), to show that e t+1 = 3e t + 2n t , we consider how new arcs are added to G t . Every arc (x, y) in G t generates one out-degree from…”

Section: Key Properties Of Complex Networkmentioning

confidence: 99%

“…Item (3) follows analogously to (2), except that we count the new bidirectional arcs once; hence, there are n t−1 many bidirectional arcs. Our next corollary gives a closed-form expression for the number of arcs in graphs generated by the ILDT model.…”

Section: Key Properties Of Complex Networkmentioning

confidence: 99%

The Iterated Local Directed Transitivity Model

Mutharasan¹

2023

Preprint

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“…In addition, the ILT model generates graphs with the small-world property, which requires graphs to have low diameter and high clustering coefficient compared to random graphs with the same number of nodes and expected average degree. A directed analogue of the ILT model was introduced in [6].…”

Section: Introductionmentioning

confidence: 99%

The Iterated Local Transitivity Model for Tournaments

Bonato¹,

Chaudhary²

2023

Preprint

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A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. We propose a new model for highly dense complex networks based on transitivity, called the Iterated Local Transitivity Tournament (or ILTT) model. In ILTT and a dual version of the model, we iteratively apply the principle of transitivity to form new tournaments. The resulting models generate tournaments with small average distances as observed in real-world complex networks. We explore properties of small subtournaments or motifs in the ILTT model and study its graph-theoretic properties, such as Hamilton cycles, spectral properties, and domination numbers. We finish with a set of open problems and the next steps for the ILTT model.

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“…Both the ILT and ILAT models were unified in the recent context of Iterated Local Models in [7]. Versions of the ILT model were considered for directed graphs [8] and hypergaphs [3], and a global version was considered in [11].…”

Section: Introductionmentioning

confidence: 99%

Iterative models for complex networks formed by extending cliques

Bonato¹,

Cushman²,

Marbach³

et al. 2022

Preprint

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We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps. For many choices of the underlying parameters, graphs generated by the model densify over time. In the special case of the cone model, generated graphs provably satisfy properties observed in real-world complex networks such as the small world property and bad spectral expansion. We finish with a set of open problems and next steps for the frustum model.

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The Iterated Local Directed Transitivity Model for Social Networks

Cited by 10 publications

References 14 publications

The Iterated Local Directed Transitivity Model

The Iterated Local Directed Transitivity Model

The Iterated Local Transitivity Model for Tournaments

Iterative models for complex networks formed by extending cliques

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