| Preface | p. v |
| Introduction | p. 1 |
| Preliminaries and Basic Definitions in Network Theory | p. 5 |
| Introduction | p. 5 |
| Basic definitions | p. 5 |
| Different kinds of graphs | p. 7 |
| Weighted, directed and oriented graphs | p. 7 |
| Subgraphs | p. 8 |
| Partited graphs | p. 9 |
| Paths and cycles | p. 9 |
| Trees | p. 10 |
| Statistics on graphs | p. 11 |
| Small world properties | p. 11 |
| Clustering coefficient | p. 12 |
| Degree distribution | p. 12 |
| Complexity | p. 14 |
| What is next | p. 15 |
| Models of Complex Networks | p. 17 |
| Introduction | p. 17 |
| Random networks | p. 18 |
| Erdos-Renyi networks | p. 18 |
| Fitness networks | p. 21 |
| Preferential attachment networks | p. 23 |
| The Barabasi-Albert model | p. 25 |
| Duplication-divergence models | p. 27 |
| Growing weighted networks | p. 30 |
| The small-world model | p. 32 |
| Outlook | p. 33 |
| Correlations in Complex Networks | p. 35 |
| Introduction | p. 35 |
| Detailed balance condition | p. 36 |
| Empirical measurement of correlations | p. 39 |
| Two vertices correlations: ANND | p. 41 |
| Three vertices correlations: Clustering | p. 45 |
| Networks in the real world | p. 47 |
| Pretty-good-privacy web of trust | p. 51 |
| Modeling correlations | p. 54 |
| Disassortative correlations | p. 55 |
| The configuration model | p. 55 |
| Growing models | p. 56 |
| Assortativity generators | p. 57 |
| Modeling clustered networks | p. 59 |
| Random graphs with attributes | p. 60 |
| Hidden color models | p. 61 |
| Fitness or hidden variables models | p. 62 |
| Fitness and preferential attachment models | p. 64 |
| Outlook | p. 65 |
| The Architecture of Complex Weighted Networks: Measurements and Models | p. 67 |
| Introduction | p. 67 |
| Tools for the characterization of weighted networks | p. 68 |
| Weights | p. 68 |
| Degree and weight distributions | p. 68 |
| Weighted degree: Strength | p. 68 |
| Weighted clustering | p. 69 |
| Weighted assortativity: Affinity | p. 70 |
| Local heterogeneity | p. 71 |
| Weighted networks: Empirical results | p. 72 |
| Transportation networks | p. 73 |
| Airport network | p. 73 |
| Urban and inter-urban movement networks | p. 77 |
| Transportation networks: Summary | p. 78 |
| Social network: Example of the scientific collaboration network | p. 79 |
| Biological network: The case of the metabolic network | p. 83 |
| Modeling weighted networks | p. 83 |
| Coupling weight and topology | p. 83 |
| A simple model: Weight perturbation and "busy get busier" effects | p. 84 |
| Local heterogeneities, nonlinearities and space-topology coupling | p. 88 |
| Other models coupling traffic and topology | p. 90 |
| Outlook | p. 91 |
| Community Structure Identification | p. 93 |
| Introduction | p. 93 |
| Definitions of communities | p. 94 |
| Evaluating community identification | p. 96 |
| Link removal methods | p. 97 |
| Shortest path centrality | p. 97 |
| Current-flow and random walk centrality | p. 98 |
| Information centrality | p. 99 |
| Link clustering | p. 100 |
| Agglomerative methods | p. 100 |
| Hierarchical clustering | p. 100 |
| L-shell method | p. 101 |
| Methods based on maximising modularity | p. 102 |
| Greedy algorithm | p. 102 |
| Simulated annealing methods | p. 102 |
| Extremal optimisation | p. 103 |
| Spectral analysis methods | p. 104 |
| Spectral bisection | p. 104 |
| Multi dimensional spectral analysis | p. 105 |
| Constrained optimisation | p. 106 |
| Approximate resistance networks | p. 106 |
| Other methods | p. 107 |
| Clustering and curvature | p. 107 |
| Random walk based methods | p. 108 |
| Q-potts model | p. 110 |
| Comparative evaluation | p. 111 |
| Conclusion | p. 113 |
| Visualizing Large Complex Networks | p. 115 |
| Introduction | p. 115 |
| Global methods for visualizing large graphs | p. 116 |
| Spring embedder based methods | p. 117 |
| Properties | p. 118 |
| Spectral layout | p. 121 |
| Properties | p. 122 |
| Analytical layouts | p. 124 |
| Centrality and status layouts | p. 125 |
| Clustered layouts | p. 126 |
| Case studies | p. 129 |
| Modeling the Webgraph: How Far We Are | p. 133 |
| Introduction | p. 133 |
| Preliminaries | p. 134 |
| WebBase | p. 137 |
| In-degree and out-degree | p. 138 |
| PageRank | p. 140 |
| Bipartite cliques | p. 141 |
| Strongly connected components | p. 142 |
| Stochastic models of the webgraph | p. 142 |
| Models of the webgraph | p. 143 |
| A multi-layer model | p. 144 |
| Large scale simulation | p. 146 |
| Algorithmic techniques for generating and measuring webgraphs | p. 149 |
| Data representation and multifiles | p. 151 |
| Generating webgraphs | p. 152 |
| Traversal with two bits for each node | p. 154 |
| Semi-external breadth first search | p. 154 |
| Semi-external depth first search | p. 155 |
| Computation of the SCCs | p. 155 |
| Computation of the bow-tie regions | p. 156 |
| Disjoint bipartite cliques | p. 157 |
| PageRank | p. 160 |
| Summary and outlook | p. 161 |
| The Large Scale Structure of the Internet | p. 162 |
| Introduction | p. 163 |
| Internet maps | p. 164 |
| Heavy tailed distributions | p. 168 |
| Sampling biases and the scale-free nature of the Internet | p. 171 |
| Hierarchies and correlations | p. 173 |
| Outlook | p. 183 |
| Spanning Trees in Ecology | p. 185 |
| Introduction | p. 185 |
| Graph-theoretical formalism | p. 186 |
| Basic notions | p. 187 |
| Connected subgraphs and minimum spanning trees | p. 188 |
| Graphs and spanning trees in ecology | p. 189 |
| Spanning trees in food webs | p. 189 |
| Spanning trees in taxonomy | p. 192 |
| Empirical results | p. 195 |
| Food webs | p. 195 |
| Taxonomic trees | p. 198 |
| Summary and outlook | p. 202 |
| Social and Financial Networks | p. 205 |
| Introduction | p. 205 |
| Social networks: Examples and general features | p. 206 |
| Degree distribution | p. 208 |
| Open questions on degree distribution | p. 210 |
| Assortativity | p. 210 |
| Open questions on assortativity | p. 212 |
| Clustering | p. 213 |
| Open questions on clustering | p. 214 |
| Community structure | p. 214 |
| Open questions on community structure | p. 216 |
| Economical networks: The case-study of the board of directors | p. 218 |
| Board and directors network as bipartite graphs | p. 220 |
| Topological properties of boards and directors Networks | p. 222 |
| Average quantities | p. 222 |
| Degree distributions and assortativity | p. 224 |
| Lobbies | p. 226 |
| Modeling boards of directors networks | p. 228 |
| Interlock structure and decision making dynamics | p. 228 |
| Single board decision making model | p. 229 |
| Multiple boards decision making model | p. 232 |
| Conclusion | p. 233 |
| References | p. 235 |
| Index | p. 249 |
| Table of Contents provided by Ingram. All Rights Reserved. |
