Analysis of a bipartite network of movie ratings and catalogue network growth models

Network science is a rapidly growing field that draws important results from mathematics, physics, computer science, sociology, and many other disciplines. There are many problems in nature and man made systems that involve interactions between large number of agents which take place over a non-trivial topology. These problems lend themselves naturally and successfully to a network representation. Of particular interest are the models that deal with growth and evolution of networks because the vast majority of the systems represented by them are not static. This work is concerned about systems with two different types of interacting constituents known as bipartite networks. This thesis is structured as follows: In Chapter 1 a network is defined as a graph and a brief introduction to the concepts used throughout this work is given. We describe the well-known network growth model of Preferential Attachment [2] and a model of the evolution of a bipartite network whose agent quantities are fixed [9]. In Chapter 2 we study data from Netflix, an online movie rental service whereby users can give ratings to movies they rent. We show how this system can be represented as a network and analyse some of its properties. The probability distribution of the number of ratings of users and movies follows a power-law distribution with an exponential cutoff, which indicates saturation in the number of ratings that a movie can receive or a user give. We also found that movies and users in the system form densely connected neighbourhoods. Chapter 3 is concerned with the development of network growth and evolution models which attempt to explain the growth and evolution of networks with saturation and a limited number of agents. We develop a network growth model in which the agents are drawn from fixed catalogues. An exact analytical solution to the model can sometimes be found, an approximate one using asymptotics in other cases and numerically in general. The results given by this model describe what is observed in simulated networks and show some of the characteristics observed in the Netflix network