Evolution of Random Networks 1000-OG-EN-ERN

https://plas.mat.umk.pl/moodle/

The purpose of the course is presentation of mathematical foundations of the contemporary theory of complex networks. The course is oriented toward dynamical aspects related to the evolution of networks in time.
1. Worm-up: Branching Processes.
- Survival versus Extinction.
- Supercritical Branching Processes.
- Poisson Branching Processes.
2. Basic facts for the Erdős-Rényi Random Graphs.
- Comparison to Branching Processes.
- The Subcritical and Supercritical Regimes.
- Central Limit Theorem for the Giant Component.
3. Review of Models for Complex Networks.
- Generalized Random Graphs.
- Configuration Models.
4. Preferential Attachment Models.
- Analysis of Degree Sequences.
- Maximal Degree.
5. Emergence of Power Laws.

Total student workload

Attendance at lectures - 30 hours On-line consultations with the lecturer – 5 hours Literature studies - 25 hours Preparations to the exam - 30 hours Razem - 90 godz.

Learning outcomes - knowledge

W1: Student’s knowledge of mathematical methods used in description of real complex networks is to be deepen (K_W01) W2: Student understands the role of mathematical formalism in verification of properties of imprecise models (K_W01)

Learning outcomes - skills

U1: Student is able to identify problems in description of complex networks (K_U01) U2: Student is able to retrieve information while searching the professional literature (K_U02)

Learning outcomes - social competencies

K1: Student appreciates intellectual honesty of her/himself and other people (K_K07) K2: Student has a good command of a professional terminology within the area covered by the lecture (K_K06)

Teaching methods

Presentation-based lecture

Expository teaching methods

- problem-based lecture

Online teaching methods

- methods developing reflexive thinking

Type of course

elective course

Prerequisites

Basic course in probability theory

Course coordinators

Adam Jakubowski

Assessment criteria

Oral exam - W1-W2, U1, K1-K2.

Practical placement

- not applicable

Bibliography

1. R. Durrett, Random Graph Dynamics, Cambridge Univ. Press, 2007.
2. R. van der Hofstad, Random Graphs and Complex Networks, Vol. I, Cambridge Univ. Press, 2017.
3. R. Lyons and Y. Peres, Probability on Trees and Networks, Cambridge Univ. Press, 2016.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1000-OG-EN-ERN in USOSweb