# Coursebooks

## Statistical analysis of network data

#### Lecturer(s) :

Olhede Sofia Charlotta

English

#### Summary

A first course in statistical network analysis and applications.

#### Content

•  Basic description of a network and its generalizations (e.g. hypergraphs).
• Network examples from a practical point of view.
• Simple network summaries such as the degree distribution.
• Sparse and dense networks. Edge versus node models.
• Statistical implications of probabilistic properties of large networks.
• Erdos Renyi networks, simple models (configuration and stochastic block models).
• Sampling properties of network summaries.
• Fitting simple network models.
• Multilayer networks and directed networks
• Hypergraphs
• Exchangeability and probabilistic symmetries.
• Other topics as time permits.

#### Keywords

• network/graph
• Erdos-Renyi, configuaration and stochastic block models
• network summaries
• sparse networks
• exchangeability

#### Learning Prerequisites

##### Required courses

• Probability and Statistics

##### Recommended courses

• Probability and Statistics for mathematicians.

##### Important concepts to start the course

• The material from first courses in probability and statistics.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Recognize when a network model is appropriate
• Compute simple network summaries
• Assess / Evaluate parameters of basic network models from data
• Assess / Evaluate a range of network models and understand their properties
• Assess / Evaluate the implications of model symmetries

#### Teaching methods

Ex cathedra lectures and exercises

Final exam.

#### Supervision

 Office hours No Assistants Yes Forum No

#### Resources

No

##### Bibliography

• R. Durrett: Random Graph Dynamics. Cambridge University Press 2007·
• E.D. Kolaczyk: Statistical Analysis of Network Data. Springer, 2009·
• Ibid Topics at the Frontier of Statistics and Network Analysis: (Re)Visiting The Foundations (SemStat Elements)·
• R. van der Hofstad. Random Graphs and Complex Networks Volume One, 2016 ·
• M. Newman: Networks: An Introduction, OUP 2010.

##### Notes/Handbook

A photocopy of the course notes will be available.

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German