Кто читает:: Факультет математики

Статус:: Курс по выбору

Когда читается:: 2-й курс, 3, 4 модуль

Преподаватель

Горбунов Василий Геннадьевич

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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

Expected Learning Outcomes

Course Contents

Introduction. Basic 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

Активность на семинарах
Доклад

Interim Assessment

2025/2026 4th module
Каждому участнику семинара необходимо сделать доклад (дедлайн выбора темы для доклада - неделя следующая после юрьевой, возможно для записавшихся заранее будет положен небольшой поощрительный бонус в оценку), по результатам которого и будет сформирована итоговая оценка

Bibliography

Recommended Core Bibliography

Теория графов, Харари, Ф., 2018

Recommended Additional Bibliography

Structural analysis of complex networks, , 2011

Authors

GORBUNOV VASILIY GENNADEVICH

Магистерская программа «Математика»

Research Seminar "Complex Networks 2"