Growing networks with mixed attachment mechanisms

To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such verification is performed by measuring citation dynamics of Physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including non-stationary citation distributions, diverging citation trajectory of similar papers, runaways or "immortal papers" with infinite citation lifetime etc. Thus, our most important finding is nonlinearity in complex network growth. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.

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“…Similar two-term growth equations were suggested by Refs. [13,29,35,36]. Equation 4 is formally identical to Eq.…”

Section: Introductionmentioning

confidence: 99%

Growing complex network of citations of scientific papers: Modeling and measurements

Golosovsky

Solomon

2017

Phys. Rev. E

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“…The aim of a wide range of network models is to provide a framework to understand how linkage mechanisms for establishing links give rise to particular topological properties, including degree distributions [4,9], clustering [33], average path lengths [1], and community partitions [26]. There has been a continuous and significant effort directed at formalizing such mechanisms and their role in the formation of networks like the Internet, the world wide web, and co-authorship associations [31,5,30,8,2,19,12,23,13,17,16,4,34].…”

Section: Introductionmentioning

confidence: 99%

“…The two mechanisms combined yield a degree distribution that asymptotically follow a power law. If the growth mechanism is combined with a uniform random attachment mechanism, with no preference for nodes with a high degree, then the resulting network follows an exponential function [30]. However, a recent study shows that from nearly 1000 empirical networks less than 5% exhibit pure power law or exponential relationships [7].…”

Section: Introductionmentioning

confidence: 99%

Estimating formation mechanisms and degree distributions in mixed attachment networks

Medina¹,

Finke²,

Rocha³

2019

J. Phys. A: Math. Theor.

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Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to random and preferential linkage with a fixed probability. Past approaches apply likelihood analysis to estimate the probability of occurrence of each mechanism at a particular network instance, exploiting the concavity of the likelihood function at each point in time. However, the probability of connecting to existing nodes, and consequently the likelihood function itself, varies as networks grow. We establish conditions under which applying likelihood analysis guarantees the existence of a local maximum of the time-varying likelihood function and prove that an expectation maximization algorithm provides a convergent estimate. Furthermore, the in-degree distributions of the nodes in the growing networks are analytically characterized. Simulations show that, under the proposed conditions, expectation maximization and maximum-likelihood accurately estimate the actual contribution of each mechanism, and in-degree distributions converge to stationary distributions.

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“…The attachment of new nodes results according to a uniform random distribution followed by the formation of triad junctions. Like [21] the formation mechanism in this paper does not instantiate the principle of preferential attachment, focusing on conditions that generate extended, rather than single, power law distributions [22], [23].…”

Section: Introductionmentioning

confidence: 99%

Structure of growing networks with no preferential attachment

Moriano

Finke

2013

2013 American Control Conference

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Based on the formation of triad junctions, the proposed mechanism generates growing networks that exhibit extended power law behavior and strong neighborhood clustering. The asymptotic behavior of both properties is of interest in the study of networks in which (i) the formation of links cannot be described according to the principle of preferential attachment; (ii) the in-degree distribution fits a power law for nodes with a high degree and an exponential form otherwise; and (iii) the degree of clustering depends on both the number of links that newly added nodes establish and the probability of forming triads.

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Growing networks with mixed attachment mechanisms

Cited by 22 publications

References 24 publications

Growing complex network of citations of scientific papers: Modeling and measurements

Growing complex network of citations of scientific papers: Modeling and measurements

Estimating formation mechanisms and degree distributions in mixed attachment networks

Structure of growing networks with no preferential attachment

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