2026/2027
Просто о сложных сетях 2
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Тужилин Михаил Алексеевич
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
The course is devoted to the fundamentals of graph theory and complex networks. It starts with the main concepts of basic graph theory and ends with its modern scientific directions.
Expected Learning Outcomes
- Graphs and useful matrices
- Metrics on graph and trees, cuts
- Electric networks and related matrices
- Adjacency matrix spectra and chromatic
- Adjacency matrix spectra and clustering, Fiedler Vector, Cheeger inequality
- Matrices and random walks
- Formulate the general problem of metrization of graphs space
- For the case of dense graphs establish their limiting objects (graphons), provide the basic theorems about graphon properties
- For the case of sparse graphs describe the concept of Benjamini-Schramm convergence
- Phase transition in Erdos-Renyi model
- Multiplicative spanners*
- Application of graphons in the investigation of dynamics on networks and spin systems
- Moon's theorem (all-minors matrix-tree theorems), graph-theoretic solutions to linear systems
- Electrical networks, Schur complement, and the combinatorics of groves
- Effective resistance metric and cut metrics
Assessment Elements
- HomeworkOur course is divided into several parts such as -Introduction to graph theory -Graphs and Matrices -Spectral graph theory -Random Graphs -Dynamics on graphs After each part the list of problems will be provided
- Exam
Interim Assessment
- 2026/2027 4th moduleFinal grade for the course – at the end of the entire course. The maximum score is 150, which is calculated as 100×W + 50×E, where W is the coursework grade (based on work throughout all four modules, including homework, seminar participation, and tests), and E is the final exam grade at the end of the year.