Research Seminar "Complex Networks 1"

2026/2027

Учебный год

ENG

Обучение ведется на английском языке

3

Кредиты

Кто читает:

Факультет математики

Статус:

Курс по выбору

Когда читается:

1-й курс, 1, 2 модуль

Преподаватель

Горбунов Василий Геннадьевич

Course Syllabus

Abstract

"The theory of complex networks is a broad scientific field that studies graphs and their evolution. Models from this theory are applied in biology, machine learning, sociology, economics, and many other areas. In our annual seminar, we discuss the main existing approaches to the analysis of both static and dynamic properties of complex networks. This year, the course will be offered as a continuation of the """"Simple Introduction to Complex Networks"""" course. It is assumed that participants already have some prior knowledge of the subject. Each participant is expected to give a presentation or conduct a pre-approved study related to the course topic over the semester. Nevertheless, several introductory lectures will be delivered by the instructors. In the first semester, we will review the fundamental concepts of complex network theory and explore several topics related to network formation through probabilistic and game-theoretic models. In the second semester, we will discuss topics related to dynamics on complex networks and attempt to address practical aspects of working with graphs and complex networks."

Learning Objectives

• To provide students with a comprehensive understanding of the fundamental concepts, probabilistic and game-theoretic formation models, dynamics on graphs, and practical aspects of analyzing static and dynamic properties of complex networks through theoretical study and individual semester-long research.

Expected Learning Outcomes

• To independently analyze static and dynamic properties of complex networks, apply probabilistic and game-theoretic models to explain network formation mechanisms, simulate processes on graphs, and conduct a semester-long research project applying advanced methods of network analysis to real-world data.

Course Contents

• Introduction. Basiс structures of complex networks and their definitions (vertex degree, centrality, motives, community structures, graph spectrum)
• Topological properties of real networks
• Basic models of complex networks
• Static and dynamic stability
• Propagation processes in networks
• Synchronization and collective dynamics, the main function of sustainability
• Algorithms for searching for community structures
• Any other topics at the request of the listeners that we have time to touch on

Assessment Elements

• Presentation
  Each participant of the seminar is required to give a presentation (the deadline for topic selection is the week following Yury’s Week; early topic selection may result in a small bonus to the final grade). The final grade will be based primarily on the presentation.
• exam

Interim Assessment

• 2026/2027 2nd module
  Each participant of the seminar is required to give a presentation (the deadline for topic selection is the week following Yury’s Week; early topic selection may result in a small bonus to the final grade). The final grade will be based primarily on the presentation.

Bibliography

Recommended Core Bibliography

• Теория графов, Татт, У., 1988

Recommended Additional Bibliography

• Structural analysis of complex networks, , 2011
• Теория графов, Омельченко, А. В., 2018
• Теория графов, Оре, О., 1980
• Теория графов, Харари, Ф., 2003

Authors

• OZHEGOV FEDOR IUREVICH
• Samoilenko Ivan Aleksandrovich
• Gorbunov Vasilii Gennadevich