F1-F5 Fundamentals of network science (5 weeks)

A1-A6 Advanced topics in network science (6 weeks)

T1-T2 Invited talks and presentations (2 weeks)

*Course overview, logistics and syllabus. Coursework description, instructions and other details.*

- F1 Course overview and syllabus
- F1 Course logistics and coursework
- F5 Course project and paper details

*From classical graph theory to social network analysis and modern network science. Graphology and networkology.*

- F1 Networks introduction and motivation
- F1 Graph theory and network science
- F2 Graphology and networkology
- F5 Networks in modern science
- A2 Network science journals
- A2 Network science events

*Random graphs and real networks. Degrees of separation in small-world networks, power-law distributions of scale-free networks and mixing in networks.*

- F2 Random graph models
- F2 Configuration graph model
- A3 Exponential random graph model
- F3 Small-world networks and models
- F3 Scale-free networks and models
- F3 Node mixing in networks

*Network community and core-periphery structure. Graph partitioning, blockmodeling and community detection. Network motifs, graphlets and node orbits.*

- F4 Weak ties and network community structure
- F4 Graph partitioning and community detection
- A1 Blockmodeling and stochastic block models
- A2 Network motifs, graphlets and node orbits

*Measures of node position and centrality, measures of link importance and bridging, and link analysis algorithms. Node similarity and equivalence.*

- F4 Measures of node centrality
- A1 Node similarity and equivalence
- A1 Measures of link bridging
- F4 Link analysis algorithms

*Generative models of network evolution and link copying models. Network optimization models and random geometric graphs.*

- A3 Models of network evolution
- A3 Network optimization models

*Network inference and link prediction methods. Network-based clustering, classification and regression. Network influence maximization and outbreak detection.*

- A5 Network inference and link prediction
- A5 Network-based clustering and classification
- A4 Network influence maximization\(^‡\)
- A4 Network outbreak detection\(^‡\)

*Fractal networks and self-similarity, network sampling, backbones and skeletons. Network comparison by fragments and statistical comparison of network metrics.*

- A2 Network self-similarity and sampling
- A3 Network backbones and skeletons
- A2 Structural network comparison

*Decentralized search and network navigation. Percolation theory and network robustness. Spreading and diffusion on networks. Game theory and networks.*

- A4 Search and network navigation\(^‡\)
- A5 Percolation and network robustness
- A5 Epidemic spreading on networks
- A4 Network diffusion and contagion\(^‡\)
- \(\times\) Game theory and networks\(^§\)

*Attributed, valued and signed networks. Multi-relational, multilayer and higher-order networks. Temporal and spatial networks.*

- \(\times\) Attributed, valued and signed networks
- \(\times\) Multi-relational and multilayer networks
- \(\times\) Higher-order dependencies in networks
- \(\times\) Temporal and spatial networks\(^§\)

*Network representations, data structures, fundamental algorithms, programming libraries and software. Node layout and network visualization.*

- F5 Network representations and data structures
- F5 Fundamental network analysis algorithms
- A1 Node layout and network visualization
- F5 Network libraries and software

*Detecting automobile insurance fraudsters. Mining software dependency networks. Comparing bibliographic databases, clustering and modeling scientific publications, and analyzing scientific coauthorships.*

- A6 Fraud detection
- A6 Software engineering
- A6 Bibliometrics & scientometrics

*Tentative list of short weekly challenges on network concepts and techniques.*

- F1 Four knights challenge
- F2 Random selection challenge
- F3 Five networks challenge
- F4 Low complexity challenge
- F5 Grand graph challenge

- A1 \(\div\)-vector centrality challenge
- A3 Prison phone book challenge
- A5 Unreal network challenge

\(^‡\)Video lecture \(^§\)Tentative talk