Time evolving Random Network Models are presented as a mathematical framework for modelling and analyzing the evolution of complex networks. This framework allows the analysis over time of several network characterizing features such as link density, clustering coefficient, degree distribution, as well as entropy-based complexity measures, providing new insight on the evolution of random networks. First, some simple dynamic network models, based only on edge density, are analyzed to serve as a baseline reference for assessing more complex models. Then, a model that depends on network structure with the aim of reflecting some characteristics of real networks is also analyzed. Such model shows a more sophisticated behavior with two different regimes, one of them leading to the generation of high clustering coefficient/link density ratio values when compared with the baseline values, as it happens in many real networks. Simulation examples are discussed to illustrate the behavior of the proposed models.
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