| Complex Networks of Urban Environments | p. 1 |
| Paradigm of a City | p. 4 |
| Cities and Humans | p. 4 |
| Facing the Challenges of Urbanization | p. 6 |
| The Dramatis Personae. How Should a City Look? | p. 9 |
| Cities Size Distribution and Zipf's Law | p. 15 |
| European Cities: Between Past and Future | p. 17 |
| Maps of Space and Urban Environments | p. 18 |
| Object-Based Representations of Urban Environments. Primary Graphs | p. 18 |
| Cognitive Maps of Space in the Brain Network | p. 19 |
| Space-Based Representations of Urban Environments. Least Line Graphs | p. 22 |
| Time-based Representations of Urban Environments | p. 24 |
| How Did We Map Urban Environments? | p. 26 |
| Structure of City Spatial Graphs | p. 28 |
| Matrix Representation of a Graph | p. 29 |
| Shortest Paths in a Graph | p. 31 |
| Degree Statistics of Urban Spatial Networks | p. 32 |
| Integration Statistics of Urban Spatial Networks | p. 35 |
| Scaling and Universality: Between Zipf and Matthew. Morphological Definition of a City | p. 37 |
| Cameo Principle of Scale-Free Urban Developments | p. 40 |
| Trade-Off Models of Urban Sprawl Creation | p. 42 |
| Comparative Study of Cities as Complex Networks | p. 46 |
| Urban Structure Matrix | p. 47 |
| Cumulative Urban Structure Matrix | p. 49 |
| Structural Distance Between Cities | p. 52 |
| Summary | p. 54 |
| Wayfinding and Affine Representations of Urban Environments | p. 55 |
| From Mental Perspectives to the Affine Representation of Space | p. 56 |
| Undirected Graphs and Linear Operators Defined on Them | p. 58 |
| Automorphisms and Linear Functions of the Adjacency Matrix | p. 58 |
| Measures and Dirichlet Forms | p. 61 |
| Random Walks Defined on Undirected Graphs | p. 62 |
| Graphs as Discrete time Dynamical Systems | p. 63 |
| Transition Probabilities and Generating Functions | p. 63 |
| Stationary Distribution of Random Walks | p. 64 |
| Continuous Time Markov Jump Process | p. 66 |
| Study of City Spatial Graphs by Random Walks | p. 66 |
| Alice and Bob Exploring Cities | p. 67 |
| Mixing Rates in Urban Sprawl and Hell's Kitchens | p. 68 |
| Recurrence Time to a Place in the City | p. 70 |
| What does the Physical Dimension of Urban Space Equal? | p. 72 |
| First-Passage Times: How Random Walks Embed Graphs into Euclidean Space | p. 74 |
| Probabilistic Projective Geometry | p. 74 |
| Reduction to Euclidean Metric Geometry | p. 76 |
| Expected Numbers of Steps are Euclidean Distances | p. 78 |
| Probabilistic Topological Space | p. 80 |
| Euclidean Embedding of the Petersen Graph | p. 80 |
| Case study: Affine Representations of Urban Space | p. 83 |
| Ghetto of Venice | p. 83 |
| Spotting Functional Spaces in the City | p. 86 |
| Bielefeld and the Invisible Wall of Niederwall | p. 86 |
| Access to a Target Node and the Random Target Access Time | p. 89 |
| Pattern of Spatial Isolation in Manhattan | p. 92 |
| Neubeckum: Mosque and Church in Dialog | p. 98 |
| Summary | p. 99 |
| Exploring Community Structure by Diffusion Processes | p. 101 |
| Laplace Operators and Their Spectra | p. 101 |
| Random Walks and Diffusions on Weighted Graphs | p. 102 |
| Diffusion Equation and its Solution | p. 103 |
| Spectra of Special Graphs and Cities | p. 104 |
| Cheeger's Inequalities and Spectral Gaps | p. 109 |
| Is the City an Expander Graph? | p. 112 |
| Component Analysis of Transport Networks | p. 114 |
| Graph Cut Problems | p. 114 |
| Weakly Connected Graph Components | p. 115 |
| Graph Partitioning Objectives as Trace Optimization Problems | p. 117 |
| Principal Component Analysis of Venetian Canals | p. 121 |
| Sestieri of Venice | p. 121 |
| A Time Scale Argument for the Number of Essential Vectors | p. 124 |
| Low-Dimensional Representations of Transport Networks by Principal Directions | p. 125 |
| Dynamical Segmentation of Venetian Canals | p. 127 |
| Thermodynamical Formalism for Urban Area Networks | p. 129 |
| In Search of Lost Time: Is there an Alternative for Zoning? | p. 129 |
| Internal Energy of Urban Space | p. 131 |
| Entropy of Urban Space | p. 132 |
| Pressure in Urban Space | p. 134 |
| Summary | p. 136 |
| Spectral Analysis of Directed Graphs and Interacting Networks | p. 137 |
| The Spectral Approach For Directed Graphs | p. 138 |
| Random Walks on Directed Graphs | p. 138 |
| A Time-Forward Random Walk | p. 138 |
| Backwards Time Random Walks | p. 139 |
| Stationary Distributions on Directed Graphs | p. 140 |
| Laplace Operator Defined on the Aperiodic Strongly Connected Directed Graphs | p. 141 |
| Bi-Orthogonal Decomposition of Random Walks Defined on Strongly Connected Directed Graphs | p. 142 |
| Dynamically Conjugated Operators of Random Walks | p. 142 |
| Measures Associated with Random Walks | p. 143 |
| Biorthogonal Decomposition | p. 144 |
| Spectral Analysis of Self-Adjoint Operators Defined on Directed Graphs | p. 146 |
| Self-Adjoint Operators for Interacting Networks | p. 148 |
| Summary | p. 150 |
| Urban Area Networks and Beyond | p. 151 |
| Miracle of Complex Networks | p. 151 |
| Urban Sprawl - a European Challenge | p. 152 |
| Ranking Web Pages, Web Sites, and Documents | p. 155 |
| Image Processing | p. 155 |
| Summary | p. 157 |
| Bibliography | p. 159 |
| Index | p. 177 |
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