Course Name
Complex Networks and Applications
What is this course about?
Background: Networks are a fundamental tool for modelling complex social, technological, and biological systems. Coupled with the emergence of online social networks and large-scale data availability in biological sciences, this course focuses on the analysis of massive networks which provide many computational, algorithmic, and modelling challenges.
Course: The course will cover recent research on the structure, analysis and applications of such large networks and on models and algorithms that abstract their basic properties. Students will explore how to practically analyse large-scale network data and how to reason about it through models for network structure and search.
Topics: Real-world networks and how we determine their structure; Algorithms that use matrix and linear algebra methods; Models of the formation of networks; Identification of functional modules in networks; Robustness and fragility of complex networks; How information spreads through networks; Methods for searching networks for particular vertices or items.
Prerequisites
Students are expected to have the following background:
Knowledge of basic computer science principles, sufficient to write a reasonably non-trivial computer program (e.g., COMP2521 or equivalent are recommended)
Familiarity with basic probability theory (e.g. COMP9020 or COMP3121 or COMP9101 or DPST1014 or MATH2801)
Familiarity with basic linear algebra (e.g. MATH2501 would be much more than necessary)
Course Materials
The following books are recommended as optional reading:
Schedule
| Week | Topic(s) |
|---|---|
| 1 | Introduction to real-world networks (technological-, social-, information-, biological- networks) |
| 2 |
Mathematics of networks Measures and metrics (centrality, transitivity, and assortativity) |
| 3 | The large-scale structure of networks (small-world effect, power-law and scale-free networks) |
| 4 | Matrix algorithms and graph partitioning |
| 5 |
Network generative models 1 (random graphs) Network generative models 2 (small-world networks, scale-free networks) |
| 6 | Nil |
| 7 | Percolation and network resilience |
| 8 | Epidemics on networks |
| 9 | Dynamical systems on networks |
| 10 | Network search |