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Explanatory Notes
Instructions
Web page:
https://moodle.fel.cvut.cz/course/view.php?id=8066
Anotation:
This course responds to an ever-increasing demand for understanding contemporary networks – large-scale complex systems composed of many components and subsystems interconnected into a single distributed entity. Herein, we will consider fundamental similarities between diverse areas such as e.g. forecasting the spread of global pandemics, public opinion dynamics and manipulation of communities through social media, formation controls for unmanned vehicles, energy generation and distribution in power grids, etc. Understanding such compelling issues goes far beyond the boundaries of any single physical, technological or scientific domain. Therefore, we will analyze phenomena across different domains, involving societal, economic and biological networks. For such networked systems, the resulting behavior depends not only on the characteristics of their individual components and details of their physical or logical interactions, but also on a precise way those components are interconnected – the detailed interconnection topology. For that reason, the first part of the course introduces fundamental theoretical and abstract computational network analysis concepts; in particular, the algebraic graph theory, network measures and metrics and fundamental network algorithms. The second part of the course subsequently views networks as dynamical systems, studies their properties and ways in which these are controlled, using mainly methods of automatic control theory.
Study targets:
Get familiar with the computational frameworks for analysis and synthesis of large-scale complex interconnected networked systems.
Content:
| 1. | | Basic network concepts and examples of technological, information, social and biological networks. |
| 2. | | Algebraic and spectral graph theory: adjacency matrix, graph Laplacian matrix, incidence matrix, paths and loops, reachability, graph matrix eigenvalues and eigenvectors; Frobenius form: reducible and irreducible components. |
| 3. | | Network measures and metrics: centralities, PageRank, similarities, clusters and communities. |
| 4. | | Algorithms for analysis of large-scale networks: breadth-first search, Dijkstra, depth-first search, Ford-Fulkerson, graph partition and community detection algorithms. |
| 5. | | Specific types of graphs and networks: random graph models, small-world networks, regular graphs, scale-free networks. Social and biological networks, leaders, complexity; resilience of networks. |
| 7. | | Network dynamics, processes on networks; epidemics and population dynamics. |
| 8. | | Consensus (agreement) in networks, synchronization, internal model principle. |
| 9. | | Formation control: controllability and observability in a graph, cooperative stability of a formation. |
| 10. | | Distributed control of multi-agent systems: stability, performance, passivity-based control. |
| 11. | | Scaling phenomena in distributed systems, string stability, mesh stability. |
| 12. | | Distributed estimation (for example, in wireless sensor networks). |
Course outlines:
| 1. | | Basic network concepts and examples of technological, information, social and biological networks. |
| 2. | | Algebraic and spectral graph theory: adjacency matrix, graph Laplacian matrix, incidence matrix, paths and loops, reachability, graph matrix eigenvalues and eigenvectors; reducible, irreducible and balanced graphs. |
| 3. | | Network measures and metrics: centralities, PageRank, similarities, clusters and communities. |
| 4. | | Algorithms for analysis of large-scale networks: breadth-first search, Dijkstra, depth-first search, Ford-Fulkerson, graph partition and community detection algorithms. |
| 5. | | Specific types of graphs and networks: random graph models, small-world networks, regular graphs, scale-free networks. Social and biological networks, leaders, complexity. Resilience of networks. |
| 7. | | Network dynamics, processes on networks; epidemics and population dynamics. |
| 8. | | Consensus (agreement) in networks, synchronization, internal model principle. |
| 9. | | Formation control: controllability and observability in a graph, cooperative stability of a formation. |
| 10. | | Distributed control of multi-agent systems: stability, performance, passivity-based control. |
| 11. | | Scaling phenomena in distributed systems, string stability, mesh stability. |
| 12. | | Distributed estimation (for example, in wireless sensor networks). |
Exercises outline:
The exercises will be dedicated to solving some computational problems together with the instructor and other students.
Literature:
These are the books on which the course has been based. Students will be expected to use the Mark Newman's book during the course, (a number of copies is available for the course students in the library):
| [1. | | ] Mark Newman. Networks: An introduction. Oxford University Press, 2010, ISBN: 9780199206650. |
| [2. | | ] Albert-László Barabási. Network Science, Cambridge University Press; 1st edition (2016), ISBN : 978-1107076266. |
Requirements:
This course partially builds on the foundations set in the following courses:
B(E)3M35LSY - Linear Systems
B(E)3M35ORR - Optimal and Robust Control
These prerequisites are recommended, however they are not strictly required. All the requisite background is covered in the Lecture Notes.
Subject is included into these academic programs:
| Page updated 21.12.2024 11:51:12, semester: Z/2024-5, Z/2025-6, L/2024-5, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |