Analysis of Complex Networks

Contents

Preface

List of Contributors

1 Entropy, Orbits, and Spectra of Graphs

Abbe Mowshowitz and Valia Mitsou

1.1 Introduction

1.2 Entropy or the Information Content of Graphs

1.3 Groups and Graph Spectra

1.4 Approximating Orbits

1.4.1 The Degree of the Vertices

1.4.2 The Point-Deleted Neighborhood Degree Vector

1.4.3 Betweenness Centrality

1.5 Alternative Bases for Structural Complexity

References

2 Statistical Mechanics of Complex Networks

Stefan Thurner

2.1 Introduction

2.1.1 Network Entropies

2.1.2 Network Hamiltonian

2.1.3 Network Ensembles

2.1.4 Some Definitions of Network Measures

2.2 Macroscopics: Entropies for Networks

2.2.1 A General Set of Network Models Maximizing Generalized Entropies

2.2.1.1 A Unified Network Model

2.2.1.2 Famous Limits of the Unified Model

2.2.1.3 Unified Model: Additional Features

2.3 Microscopics: Hamiltonians of Networks – Network Thermodynamics

2.3.1 Topological Phase Transitions

2.3.2 A Note on Entropy

2.4 Ensembles of Random Networks – Superstatistics

2.5 Conclusion

References

3 A Simple Integrated Approach to Network Complexity and Node Centrality

Danail Bonchev

3.1 Introduction

3.2 The Small-World Connectivity Descriptors

3.3 The Integrated Centrality Measure

References

4 Spectral Theory of Networks: From Biomolecular to Ecological Systems

Ernesto Estrada

4.1 Introduction

4.2 Background on Graph Spectra

4.3 Spectral Measures of Node Centrality

4.3.1 Subgraph Centrality as a Partition Function

4.3.2 Application

4.4 Global Topological ...