Abstract

CASTILLO-CASTILLO, P.; ARJONA-VILLICANA, P. D.  and  ACOSTA-ELIAS, J.. An accelerated growth model to generate complex networks with connectivity distribution slope that varies with time. Rev. mex. fis. [online]. 2019, vol.65, n.2, pp.128-132.  Epub Apr 17, 2020. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.65.128.

Many real-life complex networks have in-degree and out-degree distributions that decay as a power-law. However, the few models that have been able to reproduce both of these properties, can not reproduce the wide range of values found in real systems. Another limitation of these models is that they add links from nodes which are created into the network, as well as between nodes already present in this network. However, adding links between existing nodes is not a characteristic available in all systems. This paper introduces a new complex network growth model that, without adding links between existing nodes, is able to generate complex topologies with in-degree and out-degree distributions that decay as a power-law. Moreover, in this growth model, the ratio at which links are created is greater than the ratio at which nodes are born, which produces an accelerated growth phenomenon that can be found in some real systems, like the Internet at the Autonomous System level. This model also includes a behavior in which the slope of the in-degree distribution changes as the network grows, in other words, it is a function of time. Similar behaviors have been previously observed in some real systems, like the citation network of patents approved in the US between 1975 and 1999. However, in this latter network, the slope of the out-degree decreases as the network grows.

Keywords : Complex networks; scale-free networks; accelerated growth; Barabási model; Krapivsky-Redner model; 05.65.+b; 05.90.+m; 89.75.Fb.

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