Call number: LD2668 .T4 1985 G63 / Master of Science

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Li Pingping = 网络的结构性质及其动态过程 / 李萍萍. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 113-118). / Text in English; abstracts in English and Chinese. / Li Pingping = Wang luo de jie gou xing zhi ji qi dong tai guo cheng / Li Pingping. / Chapter 1 --- Overview --- p.1 / Chapter 2 --- Networks: A Review --- p.6 / Chapter 2.1 --- Graph Theory --- p.6 / Chapter 2.1.1 --- Degree --- p.7 / Chapter 2.1.2 --- Shortest-Path Length --- p.7 / Chapter 2.1.3 --- Clustering Coefficient --- p.8 / Chapter 2.2 --- Random Graphs --- p.9 / Chapter 2.2.1 --- Degree Distribution --- p.10 / Chapter 2.2.2 --- Shortest-Path Length --- p.11 / Chapter 2.2.3 --- Clustering Coefficient --- p.11 / Chapter 2.2.4 --- Shortcomings of The Model --- p.12 / Chapter 2.3 --- Small-World Network --- p.14 / Chapter 2.3.1 --- Small-World Effect in Real-World Networks --- p.14 / Chapter 2.3.2 --- Watts-Strogatz Model --- p.16 / Chapter 2.3.3 --- Properties --- p.17 / Chapter 2.3.4 --- Newman-Watts Model --- p.23 / Chapter 2.4 --- Scale-Free Network --- p.24 / Chapter 2.4.1 --- Background --- p.24 / Chapter 2.4.2 --- The Barabasi-Albert Model --- p.25 / Chapter 2.4.3 --- Shortest-Path Length --- p.28 / Chapter 2.4.4 --- Clustering Coefficient --- p.28 / Chapter 2.5 --- Summary --- p.29 / Chapter 3 --- Clustering Coefficient in Complex Networks --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Barabasi-Albert Networks --- p.32 / Chapter 3.3 --- Random Growing Networks --- p.37 / Chapter 3.4 --- Hybrid Networks with both Preferential and Random Attachments --- p.40 / Chapter 3.5 --- Summary --- p.42 / Chapter 4 --- Voter Model --- p.44 / Chapter 4.1 --- Introduction --- p.44 / Chapter 4.2 --- Voter Model --- p.45 / Chapter 4.3 --- Conservation Laws --- p.46 / Chapter 4.4 --- Ordering Process on Complex Networks --- p.47 / Chapter 4.5 --- Effective Dimension --- p.51 / Chapter 4.6 --- Summary --- p.52 / Chapter 5 --- Opinion Formation in Newman-Watts Networks --- p.54 / Chapter 5.1 --- Introduction --- p.54 / Chapter 5.2 --- Majority Rule Model in Newman-Watts Networks --- p.56 / Chapter 5.3 --- Shortening of Consensus Time --- p.58 / Chapter 5.4 --- Shortcuts and Mean-Field Limit --- p.61 / Chapter 5.5 --- Consensus Time and Shortest-Path Length --- p.65 / Chapter 5.6 --- Summary --- p.67 / Chapter 6 --- Opinion Formation in Hierarchical Networks --- p.68 / Chapter 6.1 --- Hierarchical Networks --- p.69 / Chapter 6.2 --- Shortest-Path Length --- p.72 / Chapter 6.3 --- Dynamics of Opinion Formation Model --- p.74 / Chapter 6.4 --- Summary --- p.81 / Chapter 7 --- An Introduction to Iterated Games --- p.82 / Chapter 7.1 --- Background --- p.82 / Chapter 7.2 --- Matrix Games --- p.83 / Chapter 7.3 --- The Prisoner's Dilemma --- p.85 / Chapter 7.4 --- Iterated Prisoner's Dilemma --- p.87 / Chapter 7.5 --- Evolutionary Game Theory --- p.90 / Chapter 7.5.1 --- Games in a Well-Mixed Population --- p.91 / Chapter 7.5.2 --- Games in Spatial Structure --- p.92 / Chapter 7.6 --- The Snowdrift Game --- p.92 / Chapter 8 --- Stochastic Reactive Strategies in Infinitely Iterated Games --- p.95 / Chapter 8.1 --- The PD and SD Games --- p.95 / Chapter 8.2 --- Stochastic Reactive Strategies --- p.97 / Chapter 8.3 --- Evolution of Stochastic Strategies --- p.100 / Chapter 8.4 --- Stochastic Strategies in Infinitely IPD --- p.101 / Chapter 8.5 --- Summary --- p.107 / Chapter 9 --- Summary --- p.109 / Bibliography --- p.113

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Let G = (V,A,E) be a mixed graph and co : V → {1, 2,...,λ} a function such that co is a proper colouring of the underlying graph, Und(G), and co(u) ≠ co(y) when co(v) = co(x), for every pair of arcs (u,v) and (x,y). Such a function is called a proper oriented λ − colouring of G. The number of proper oriented λ–colourings of G, denoted fo(G,λ), is a polynomial in λ. We call fo(G,λ) the mixed-chromatic polynomial of G. In this thesis we will first present the basic theory of the mixed-chromatic poly-nomial. This theory will include computational tools and results concerning the coefficients of fo(G,λ). Next, we will consider the question of chromatic uniqueness and invariance of mixed graphs. Lastly, we reformulate a contract-delete recurrence for chromatic polynomials in order to enumerate various colourings, such as k−frugal λ−colourings. / Graduate

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The object of this paper is to investigate the behavior of some important graph properties and to statistically analyze the execution times of certain graph are the average degree of a vertex, connectivity of a graph, the existence of Hamilton cycles, Euler tours, and bipartitions in graphs. This study is unique in that it is based on statistical rather than deterministic methods.