Impact of several microscopic processes in the growth and evolution of Complex Networks

Abstract

Networks are present in many aspects of our daily lives. For example, Communication Networks as telephone networks, Social Networks as Facebook and Twitter, airline networks, road networks, Internet, and WWW. The networks can be modeled using the tools of the graph theory. For example in a network of papers citations, the vertices are the papers and the edges the citation between them; in a network of web pages, the vertices are the web pages and the edges are the hyperlinks pointing from one page to another; and similarly for friendship networks, epidemic networks, communication networks, etc. The Real networks are commonly termed Complex Networks because have been demonstrated that they have properties more complex than classical random graphs. One motivation for study networks, is to decipher the local processes that originate a particular behavior between its components and to predict wanted or unwanted effects. For example, it would be important to predict how quickly an epidemic evolves and determinate how the mechanisms of the network can be used to stop or eradicate it. With the aim of to decipher the local processes that originate the topological and dynamical properties of Complex Networks, in the literature can be found many growth and evolution models. However, at this time do not exists a general model of network growth that, with the incorporation of the appropriate processes, to be able to reproduce the properties found in real-world complex networks. This is due to in the growth and evolution of complex networks exists unknown process that shape the topological and dynamical properties of this class of networks. In this Thesis, is investigated the impact that some local processes have in the topological properties of Complex Networks. Also are proposed five growth models that reproduce some properties founded in real Complex Networks.