A Guide To Temporal Networks

✍ Scribed by Naoki Masuda , Renaud Lambiotte

• Publisher: World Scientific
• Year: 2016
• Tongue: English
• Leaves: 300
• Series: Series in Complexity Science 6
• Edition: 2
• Category: Library

✦ Table of Contents

Contents
Preface to the second edition
Preface
1. Introduction
2. Mathematical toolbox
2.1 Probability
2.1.1 Discrete variables
2.1.2 Continuous variables
2.2 Renewal processes
2.2.1 Poisson processes
2.2.2 General renewal processes
2.3 Random walks and diffusion
2.3.1 Discrete time
2.3.2 Continuous time
2.4 Power-law distributions
2.5 Maximum likelihood
2.6 Entropy, information and similarity measures
2.7 Matrix algebra
2.8 Linear stability
2.9 Markov chains
2.10 Branching processes
3. Static networks
3.1 Definition
3.2 Degree distribution
3.3 Measures derived from walks and paths
3.4 Clustering coefficient
3.5 Spectral properties
3.6 Discrete-time random walks on networks
3.7 Centrality
3.7.1 Closeness centrality
3.7.2 Betweenness centrality
3.7.3 Katz centrality
3.7.4 Eigenvector centrality
3.7.5 PageRank
3.8 Models of networks
3.8.1 Erdos–Rényi random graph
3.8.2 Configuration model
3.8.3 Growing network with preferential attachment
3.9 Network motifs
3.10 Community detection
3.10.1 Modularity
3.10.2 Markov stability
3.10.3 Infomap
3.10.4 Overlapping communities
4. Analysis of temporal networks
4.1 Definition
4.1.1 Event-based representation
4.1.2 Snapshot representation
4.1.3 Other representations
4.2 Temporal walks and paths
4.2.1 Definition
4.2.2 Temporal distances
4.2.3 Vector clock
4.3 Components
4.4 Triangle counts
4.4.1 Temporal coherence of a triangle
4.4.2 Clustering coefficient
4.5 Centrality
4.5.1 Time-independent centrality
4.5.1.1 Temporal closeness
4.5.1.2 Temporal betweenness
4.5.1.3 Dynamical communicability
4.5.1.4 TempoRank
4.5.2 Time-dependent centrality
4.5.2.1 Exponential discounting in time
4.5.2.2 Running broadcast and receive centrality
4.5.2.3 Dynamic win–lose score
4.5.2.4 Eigenvector-based centralities for temporal networks
4.6 Statistical properties of event times
4.6.1 Distribution of inter-event times
4.6.2 Coefficient of variation
4.6.3 Local variation
4.6.4 Detrending
4.6.5 Fano factor
4.6.6 Detrended fluctuation analysis
4.7 Temporal correlation
4.8 Null models and randomization procedures
4.9 Temporal motifs
4.10 Detection of change points and anomalies
4.10.1 Methods based on statistical hypothesis testing and network distance measures
4.10.2 Bayesian approach to change-point detection
4.10.3 System-state dynamics of temporal networks
4.11 Link prediction
4.12 Network embedding
4.13 Communities in temporal networks
4.13.1 Modularity maximization under estrangement constraint
4.13.2 Community matching approach
4.13.3 Mapping change
4.13.4 Model-based approach
4.13.5 Multilayer modularity
4.13.6 Tensor factorization approach
4.14 Temporal networks from multivariate time series
5. Models of temporal networks
5.1 Models of non-Markovianity
5.2 Stochastic temporal networks
5.3 Activity-driven model
5.4 Priority queue models
5.5 Self-exciting processes
5.5.1 Hawkes processes
5.5.2 Cascading Poisson processes
5.6 Markovian log-linear models
5.7 Memory networks
5.8 Metapopulation model
6. Dynamics on temporal networks
6.1 Waiting-time paradox
6.2 Gillespie algorithms
6.2.1 Original Gillespie algorithm
6.2.2 Non-Markovian Gillespie algorithm
6.2.3 Laplace Gillespie algorithm
6.3 Random walks
6.3.1 Node-centric random walks
6.3.2 Edge-centric random walks
6.4 Epidemic processes
6.4.1 Models of epidemic processes
6.4.2 SIS dynamics on metapopulation models
6.4.3 SIS dynamics on switching networks
6.4.4 SIR dynamics on the neighbour exchange network model
6.4.5 Viral spreading dynamics under bursty interaction
6.4.6 SIR dynamics on a tree-like stochastic temporal network
6.5 Synchronization
6.6 Network controllability
Appendix A Discrete-time random walks on the line
Appendix B Transient and absorbing states of Markov chains
Appendix C Derivation of the degree distribution of the Barab´asi–Albert (BA) model
Bibliography
Index