A first course in network theory

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关键词：network Course Theory First FIRS network course

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飞天玄舞6 发表于 2016-12-9 10:31
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Contents
12345Introduction to Network Theory
1.1 Overview of networks
1.2 History of graphs
1.3 What you will learn from this book
Further reading
General Concepts in Network Theory
2.1 Formal definition of networks
2.2 Elementary graph theory concepts
2.3 Networks and matrices
2.4 Network connectivity
2.5 Graph structures
Further reading
How To Prove It
3.1 Motivation
3.2 Draw pictures
3.3 Use induction
3.4 Try to find a counterexample
3.5 Proof by contradiction
3.6 Make connections between concepts
3.7 Other general advice
Further reading
Data Analysis and Manipulation
4.1 Motivation
4.2 Sources of error
4.3 Processing data
4.4 Data statistics and random variables
4.5 Experimental tools
Further reading
Algebraic Concepts in Network Theory
5.1 Basic definitions of networks and matrices
5.2 Eigenvalues and eigenvectors
Further reading
6789101112Contents
Spectra of Adjacency Matrices
6.1 Motivation
6.2 Spectral analysis of simple networks
6.3 Spectra and structure
6.4 Eigenvectors of the adjacency matrix
Further reading
The Network Laplacian
7.1 The graph Laplacian
7.2 Eigenvalues and eigenvectors of the graph Laplacian
Further reading
Classical Physics Analogies
8.1 Motivation
8.2 Classical mechanical analogies
8.3 Networks as electrical circuits
Further reading
Degree Distributions
9.1 Motivation
9.2 General degree distributions
9.3 Scale-free networks
Further reading
Clustering Coefficients of Networks
10.1 Motivation
10.2 The Watts–Strogatz clustering coefficient
10.3 The Newman clustering coefficient
Further reading
Random Models of Networks
11.1 Motivation
11.2 The Erdös–Rényi model of random networks
11.3 The Barabási–Albert model
11.4 The Watts–Strogatz model
Further reading
Matrix Functions
12.1 Motivation
12.2 Matrix powers
12.3 The matrix exponential
12.4 Extending matrix powers
12.5 General matrix functions
Further reading
13141516171819Fragment-based Measures
13.1 Motivation
13.2 Counting subgraphs in networks
13.3 Network motifs
Further reading
Classical Node Centrality
14.1 Motivation
14.2 Degree centrality
14.3 Closeness centrality
14.4 Betweenness centrality
Further reading
Spectral Node Centrality
15.1 Motivation
15.2 Katz centrality
15.3 Eigenvector centrality
15.4 Subgraph centrality
Further reading
Quantum Physics Analogies
16.1 Motivation
16.2 Quantum mechanical analogies
16.3 Tight-binding models
16.4 Some specific quantum-mechanical systems
Further reading
Global Properties of Networks I
17.1 Motivation
17.2 Degree–degree correlation
17.3 Network reciprocity
17.4 Network returnability
Further reading
Global Properties of Networks II
18.1 Motivation
18.2 Network expansion properties
18.3 Spectral scaling method
18.4 Bipartivity measures
Further reading
Communicability in Networks
19.1  Motivation
19.2  Network communicability
19.3 Communicability distance
Further reading
20 Statistical Physics Analogies
20.1 Motivation
20.2 Thermodynamics in a nutshell
20.3 Micro-canonical ensembles
20.4 The canonical ensemble
20.5 The temperature in network theory
Further reading
21 Communities in Networks
21.1 Motivation
21.2 Basic concepts of communities
21.3 Network partition methods
21.4 Clustering by centrality
21.5 Modularity
21.6 Communities based on communicability
21.7 Anti-communities
Further reading