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Lecturer(s)
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Ženčák Pavel, RNDr. Ph.D.
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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1. Basic combinatorics and its applications in natural sciences and in practical problems. The first motivation for probability. 2. Motivation for complex networks (technological, social, information, biochemical networks). 3. Basic knowledge about graphs: representations, basic types of graphs, their properties and their use in practice. Evaluated graphs, oriented graphs and their properties. Eulerian graphs and Hamiltonian graphs, formulation of the tasks of a Chinese postman and a business traveler. Searching graphs in depth, in width. 4. Calculation of the shortest paths (Dijsktr algorithm, Floyd-Warshall algorithm). Acyclic graphs, graph skeleton and principles of skeleton search algorithms. Edge and vertex coloring of the graph. 5. Characteristics of complex networks: degree of peak, centrality, assortative mixing. The first look at the distribution of characteristics in large networks.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Demonstration
- Attendace
- 52 hours per semester
- Preparation for the Exam
- 60 hours per semester
- Homework for Teaching
- 20 hours per semester
- Preparation for the Course Credit
- 40 hours per semester
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Learning outcomes
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The purpose of the course is to introduce students to the basics of combinatorics, to supplement the knowledge of the basics of graph theory and to present a more modern view of graphs and networks as complex systems.
Understanding Understand the basics of combinatorics, graph theory and their perception as complex systems.
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Prerequisites
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Basic skills.
KAG/LA1A
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Assessment methods and criteria
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Oral exam, Written exam, Student performance
Combination of written and oral exam.
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Recommended literature
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Online přednáška.
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Online přednáška.
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D. Jungnickel. (2013). Graphs, Networks and Algorithms. Springer Berlin Heidelberg.
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J. Matoušek a J. Nešetřil. (2002). Kapitoly z diskrétní matematiky. Karolinum.
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Jean-Claude Fournier. (2013). Graph Theory and Applications with Exercises and Problems. Wiley-ISTE.
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L. Barabási. (2018). Network science. Cambridge University Press.
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Mark E Newman. (2010). Networks: An Introduction. Oxford University Press.
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