Network description of dynamical systems: The clustering coefficent

Abstract

[eng] In this MSc thesis, we focus on studying the different types of clustering for a flow network. A flow network is a network representation of a dynamical system. The methodology to obtain these kind of networks is relatively new and it still has many aspects to study. The motivation of this work was to verify a hypothesis dropped in Ref.[4] which theorized about the meaning of the undirected clustering for a flow network. More specifically, it was hypothesized that the undirected clustering of a flow network characterizes the stable manifolds of the dynamical system underlying it. First, we expose the different concepts of the theoretical framework involved: elements of dynamical systems theory and of network theory, mainly the different definitions of clustering. At the successive sections we show the results of our computations for the Lorenz model. In the process, we prove the motivation hypothesis to be incorrect. We continue by studying the different types of directed clustering that constitute the undirected clustering, connecting them to the properties of the dynamical system. Finally, we discuss the possible meanings of the quantities studied.