Topics and materials -- Social and technological networks
Topic 0 : Background
The background concepts used in this course are quite general. You will find many resources online to look up. Wikipedia is a good source for specific definitions. Check that you know or can understand from wikipedia and other sources (most of) the following concepts.
You are free to use your favourite books.
Graph theory
Background Concepts:
- Graphs
- Bipartite graphs
- Walks and Paths
- Breadth first search and Depth First search
- Connected components
- Shortest paths and Dijkstra's algorithm
- Spanning trees and minimum spanning trees. Kruskal's algorithm.
- Planar graphs
- Graph coloring. Four color theorem (not the proof, only the theorem statement.)
- Directed graphs and strongly connected components
There is of course wikipedia. There are many other sources online, for example:
Asymptotic notations
Concepts
Sources: Wikipedia. Also, Page 43-48 in this book.
Probablity
- Basic probability
- Expectations
- Union bound
Sources: Wikipedia.
Background problems
Topic 1: Introduction
Topic 2 : Random graphs
Topic 3 : Cascades
Topic 4 : Influence maximisation (submodular optimisation)
Topic 5 : Web graphs and Ranking pages
Topic 6: Distances and Metrics
Topic 7: Growth, Expansion and Doubling dimension of metrics
Topic 8: Community detection
Topic 9: Spectral methods
Topic 10: Strong and weak ties
Topic 11: Kernel methods and graph kernels
Topic 12: Power law networks
Topic 13: Small world networks
Topic 14: Spanners
Topic 15: Epidemics and gossip
- Slides
- Reading
- Additional (optional) reading
Topic 16: Miscellaneous (optional, not in exam)
Topic 17: Final discussion: course and exam