Node Degree Dynamics in Complex Networks Generated in Accordance with a Modification of the Triadic Closure Model

Sidorov, Sergei; Mironov, Sergei V.; Faizliev, Alexey; Grigoriev, Alexey

doi:10.1007/978-3-030-78759-2_12

Cited by 1 publication

(3 citation statements)

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“…In this section, we describe and study a development of triadic closure model proposed by P. Holme and B. J. Kim [2]. The authors of [39] develop a model describing the growth of a network, in which one node and two links are added at each iteration, and this node is connected by two links with neighboring nodes. In this section, we will extend this model in two ways.…”

Section: The Model Descriptionmentioning

confidence: 99%

“…• (b2) With probability 1 − p, a link is established with one of the network nodes s (not necessarily adjacent to node i) with a probability proportional to the degree of this node k s (t). The proposed model is extension of the growth network model presented in paper [39]; if we take m = 2 then we obtain the model studied in [39] as a particular case of our model.…”

Section: The Model Descriptionmentioning

confidence: 99%

“…where c is a constant satisfying the initial condition k i (i) = m. Equation ( 9) shows the expected temporal trajectory for the degree of an individual node i. If m = 2 and p = 1, then we obtain the dynamics (11) of the simple model described in paper [39]. The exponents β i have disparate values, which is completely different for the Barabási-Albert model.…”

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confidence: 99%

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Network Evolution Model with Preferential Attachment at Triadic Formation Step

Sidorov,

Emelianov,

Mironov

et al. 2024

Mathematics

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It is recognized that most real systems and networks exhibit a much higher clustering with comparison to a random null model, which can be explained by a higher probability of the triad formation—a pair of nodes with a mutual neighbor have a greater possibility of having a link between them. To catch the more substantial clustering of real-world networks, the model based on the triadic closure mechanism was introduced by P. Holme and B. J. Kim in 2002. It includes a “triad formation step” in which a newly added node links both to a preferentially chosen node and to its randomly chosen neighbor, therefore forming a triad. In this study, we propose a new model of network evolution in which the triad formation mechanism is essentially changed in comparison to the model of P. Holme and B. J. Kim. In our proposed model, the second node is also chosen preferentially, i.e., the probability of its selection is proportional to its degree with respect to the sum of the degrees of the neighbors of the first selected node. The main goal of this paper is to study the properties of networks generated by this model. Using both analytical and empirical methods, we show that the networks are scale-free with power-law degree distributions, but their exponent γ is tunable which is distinguishable from the networks generated by the model of P. Holme and B. J. Kim. Moreover, we show that the degree dynamics of individual nodes are described by a power law.

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Section: The Model Descriptionmentioning

confidence: 99%

Section: The Model Descriptionmentioning

confidence: 99%