Estudo de redes complexas e Mecânica Estatística não-extensiva

Abstract

When systems composed of numerous components that interact with each other and from that interaction emerge a collective behavior, phenomena due to the set, which would not be found if we considered each component individually, we call these complex systems. Social networks, where people cooperate with each other, communicating using cell phones which also interact with other cell phones through transmission antennas. The brain formed of neurons, molecules formed of atoms, the network of internet pages, WWW, where pages communicate by hyperlinks, the climate of a region, formed by air masses, are some examples of complex systems. In short, Complex Systems is the study of how parts of a system, interacting with each other, lead to collective behaviors. Therefore, we proposed to study some complex networks, especially one, given by the q-Exponential distribution, which emerges naturally during the process of maximization of Tsallis entropy. Based on the study of networks already known such as Random Networks, Small World Networks and Scale Free Networks, we try to characterize this network based on measures defined above these networks, such as the average shortest path, the clustering coefficient. In addition we observe how the shortest path behaves when we increase the size of the system. Many of these measures have already been calculated in Scale Free Networks, however, our system is directly connected to the Non-extensive Statistical Mechanics proposed by Tsallis. Thus we want to observe how the networks generated by the q-Exponential distribution behave towards this connection.