An accelerated growth model to generate complex networkswith connectivity distribution slope that varies with time

摘要

Many real-life complex networks have in-degree and out-degree distributions that decay as a power-law. However, the few models that havebeen able to reproduce both of these properties, can not reproduce the wide range of values found in real systems. Another limitation ofthese 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 networkgrowth model that, without adding links between existing nodes, is able to generate complex topologies with in-degree and out-degreedistributions that decay as a power-law. Moreover, in this growth model, the ratio at which links are created is greater than the ratio atwhich nodes are born, which produces an accelerated growth phenomenon that can be found in some real systems, like the Internet at theAutonomous 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 ofpatents approved in the US between 1975 and 1999. However, in this latter network, the slope of the out-degree decreases as the networkgrows.