Methods from the google matrix forr real complex networks analysis ; Analyse de réseaux complexes réels via des méthodes issues de la matrice de Google

In a current period where people use more and more the Internet and are connected worldwide, our lives become easier. The Network science, a recent scientific domain coming from graph theory, handle such connected complex systems. A network is a mathematical object consisting in a set of interconnected nodes and a set of links connecting them. We find networks in nature such as networks of mycelium which grow underground and are able to feed their cells with organic nutrients located at low and long range from them, as well as the circulation system transporting blood throughout the human body. Networks also exist at a human scale where humans are nodes of such networks. In this thesis we are interested in what we call real complex networks which are networks constructed from databases. We can extract information which is normally hard to get since such a network might contain one million of nodes and one hundred times more links. Moreover, networks we are going to study are directed meaning that links have a direction. One can represent a random walk through a directed network with the use of the so-called Google matrix. The PageRank is the leading eigenvector associated to this stochastic matrix and allows us to measure nodes importance. We can also build a smaller Google matrix based on the Google matrix and a subregion of the network. This reduced Google matrix allows us to extract every existing links between the nodes composing the subregion of interest as well as all possible indirect connections between them by spreading through the entire network. With the use of tools developed from the Google matrix, especially the reduced Google matrix, considering the network of Wikipedia's articles we have identified interactions between universities of the world as well as their influence. We have extracted social trends by using data related to actual Wikipedia's users behaviour. Regarding the World Trade Network, we were able to measure economic response of the European Union to external petroleum and gas price ...