The Structure of Complex Networks

THIS dissertation regards the structure of large complex networks. The dissertation is divided into three main parts. Part I contains chapters 1– 3. Part II contains chapters 4–6. Part III consists of the concluding chapter 7 and the bibliography. Part I serves as an introduction. Chapters 1 and 2 directed toward enabling a general reader to understand the concepts and nomenclature used in the research, presented in Part II of the dissertation. These chapters also motivate and explain the unifying idea behind the research contained in this dissertation. Chapter 3 describes the origin and general structure of the data set used in the subsequent chapters. Part II contains five papers that chronicle my research as a Ph.D.-student. • Chapter 4 consists of two papers: Life, Death, and Preferential Attachment [54] and Live and Dead Nodes [53] where a mathematical model of the network of scientific papers is motivated empirically and solved analytically. The model is an augmentation of the growing networks model, first introduced by Barabási and Albert [10]. In [53,54], the idea that network nodes can ‘die’, is introduced, and the associated consequences for the growth model are explored. Further, it is demonstrated that the mechanism for ‘node-death’, alone, can create networks with power-law degree distributions. • Chapter 5 concerns the longitudinal correlations, in the citation network, that is induced by the authors of the scientific papers. This chapter also contains two papers: Measures for Measures [56] and A Quantitative Analysis of Measures of Quality [57]. Here, Bayesian statistics are employed to analyze several different measures of quality. Using scaling arguments, it is demonstrated how many papers are needed to draw conclusions, regarding long-term scientific performance with usefully small statistical uncertainties. Further, the approach described here permits the value-free (i.e., statistical) comparison of scientists working in distinct areas of science. • Chapter 6 discusses the detection of communities in large networks, using deterministic mean field methods. Further, the paper, Deterministic Sune Lehmann Jørgensen 2007 Version: June 19, 2007 22:27 viii The Structure of Complex Networks Community Detection [52] presents an analytical analysis of a simple class of random networks, with adjustable community structure. Part III consists of a final, concluding chapter that recapitulates the main ideas, presented in this dissertation, and points towards new avenues for further research. Additionally, part III also contains the bibliography. Version: June 19, 2007 22:27 Sune Lehmann Jørgensen 2007 The Structure of Complex Networks ix