Abstract
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.
Highlights
A large variety of complex systems can be analyzed by constructing a model that relies on some network structure [1,2,3,4]
The first type corresponds to dynamic graphs that follow evolution laws defined explicitly on the network [5,6,7,8]; the second type gathers dynamical systems where the state variables are defined on a network [9,10]; the third type refers to co-evolution models that combine evolving networks and dynamical systems
We first characterize the basic features of some simple models of evolving networks whose evolution does not depend on network structure; the time evolution of these features serves as a reference baseline signature of the behavior of simple models
Summary
A large variety of complex systems can be analyzed by constructing a model that relies on some network structure [1,2,3,4]. We first characterize the basic features of some simple models of evolving networks whose evolution does not depend on network structure; the time evolution of these features serves as a reference baseline signature of the behavior of simple models. A model that makes use of network structure is proposed to reflect some real network characteristics The analysis of this model shows several regimes that indicate a sophisticated behavior; for some regime, the network reaches a high clustering coefficient/link density ratio [13] (when compared to the ratio values of baseline signatures), a common feature in many real networks. The paper is organized as follows: Section 2 presents the general framework for Dynamic Network
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