Latora V. et al. Complex Networks: Principles, Methods and Applications

Cambridge University Press, 2017. — 575 p. — ISBN: 978-1-107-10318-4.Networks constitute the backbone of complex systems, from the human brain to computer communications, transport infrastructures to online social systems and metabolic reactions to financial markets. Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world. Rigorous and thorough, this textbook presents a detailed overview of the new theory and methods of network science. Covering algorithms for graph exploration, node ranking and network generation, among the others, the book allows students to experiment with network models and real-world data sets, providing them with a deep understanding of the basics of network theory and its practical applications. Systems of growing complexity are examined in detail, challenging students to increase their level of skill. An engaging presentation of the important principles of network science makes this the perfect reference for researchers and undergraduate and graduate students in physics, mathematics, engineering, biology, neuroscience and the social sciences.True PDFGraphs and Graph Theory
What Is a Graph?
Directed, Weighted and Bipartite Graphs
Basic Definitions
Trees
Graph Theory and the Bridges of Königsberg
How to Represent a Graph
What We Have Learned and Further ReadingsCentrality Measures
The Importance of Being Central
Connected Graphs and Irreducible Matrices
Degree and Eigenvector Centrality
Measures Based on Shortest Paths
Movie Actors
Group Centrality
What We Have Learned and Further ReadingsRandom Graphs
Erdos and Rényi (ER) Models
Degree Distribution
Trees, Cycles and Complete Subgraphs
Giant Connected Component
Scientific Collaboration Networks
Characteristic Path Length
What We Have Learned and Further ReadingsSmall-World Networks
Six Degrees of Separation
The Brain of a Worm
Clustering Coefficient
The Watts–Strogatz (WS) Model
Variations to the Theme
Navigating Small-World Networks
What We Have Learned and Further ReadingsGeneralised Random Graphs
The World Wide Web
Power-Law Degree Distributions
The Configuration Model
Random Graphs with Arbitrary Degree Distribution
Scale-Free Random Graphs
Probability Generating Functions
What We Have Learned and Further ReadingsModels of Growing Graphs
Citation Networks and the Linear Preferential Attachment
The Barabási–Albert (BA) Model
The Importance of Being Preferential and Linear
Variations to the Theme
Can Latecomers Make It? The Fitness Model
Optimisation Models
What We Have Learned and Further ReadingsDegree Correlations
The Internet and Other Correlated Networks
Dealing with Correlated Networks
Assortative and Disassortative Networks
Newman’s Correlation Coefficient
Models of Networks with Degree–Degree Correlations
What We Have Learned and Further ReadingsCycles and Motifs
Counting Cycles
Cycles in Scale-Free Networks
Spatial Networks of Urban Streets
Transcription Regulation Networks
Motif Analysis
What We Have Learned and Further ReadingsCommunity Structure
Zachary’s Karate Club
The Spectral Bisection Method
Hierarchical Clustering
The Girvan–Newman Method
Computer Generated Benchmarks
The Modularity
A Local Method
What We Have Learned and Further ReadingsWeighted Networks
Tuning the Interactions
Basic Measures
Motifs and Communities
Growing Weighted Networks
Networks of Stocks in a Financial Market
What We Have Learned and Further ReadingsProblems, Algorithms and Time Complexity
A Simple Introduction to Computational Complexity
Elementary Data Structures
Basic Operations with Sparse Matrices
Eigenvalue and Eigenvector Computation
Computation of Shortest Paths
Computation of Node Betweenness
Component Analysis
Random Sampling
Erdos and Rényi Random Graph Models
The Watts–Strogatz Small-World Model
The Configuration Model
Growing Unweighted Graphs
Random Graphs with Degree–Degree Correlations
Johnson’s Algorithm to Enumerate Cycles
Motifs Analysis
Girvan–Newman Algorithm
Greedy Modularity Optimisation
Label Propagation
Kruskal’s Algorithm for Minimum Spanning Tree
Models for Weighted Networks
List of Programs