Uma introdução à Teoria dos Grafos e à Ciências de Redes Complexas

Abstract

Complex Network is a mathematical model applied in several practical problems, such as airplane routes between airports, connections between subway stations, interactions

in social networks, bibliographic citations in articles, scientific projects, and even in in- teractions between neural network proteins. The study of complex networks consists of

understanding how each element of this network relates to the others, as well as the be- havior of the network as a whole. Graphs are the mathematical tool used to model these

real networks, therefore studies of this theory are necessary. For this, we will make an introductory bibliographical study about graph theory, presenting a brief history of the Könisgberg Bridge Problem and Euler’s solution that started Graph Theory, the basic definitions about the elements of a graph and about some graph types. We will also present the definitions of some elements and types of Networks, the topologies of Regular Networks, Random Networks, Small World Network Model and Scale Free Networks. And finally, we will present the following measures used in the characterization of networks: the Measures of Connectivity, Measures related to Cycles, Measures of Distances and Measures of Centralities