General Prerequisites: None, though some ideas from linear algebra, graph theory and probability courses, as well as some computational experience, can be useful. However, the course is self-contained and none of these courses are required.
Course Overview: Network Science provides generic tools to model and analyse systems in a broad range of disciplines, including biology, computer science and sociology. This course aims at providing an introduction to this interdisciplinary field of research, by integrating tools from graph theory, statistics and dynamical systems. Most of the topics to be considered are active modern research areas.
Lecturer(s):
Prof. Renaud Lambiotte
Assessment Type:
Mini Project. Mini-projects will be available for collection from 12noon on Friday of week 8 and the submission deadline will be 12noon on Wednesday of week 11.
Learning Outcomes: Students will have developed a sound knowledge and appreciation of some of the tools, concepts, models, and computations used in the study of networks. The study of networks is predominantly a modern subject, so the students will also be expected to develop the ability to read and understand current (2017) research papers in the field.
Course Synopsis: 1. Introduction and short overview of useful mathematical concepts (2 lectures): Networks as abstractions; Renewal processes; Random walks and diffusion; Power-law distributions; Matrix algebra; Markov chains; Branching processes.
2. Basic structural properties of networks (2 lectures): Definition; Degree distribution; Measures derived from walks and paths; Clustering coefficient; Centrality Measures; Spectral properties.
3. Models of networks (2 lectures): Erdos-Rényi random graph; Configuration model; Network motifs; Growing network with preferential attachment.
4. Community detection (2 lectures): Newman-Girvan Modularity; Spectral optimization of modularity; Greedy optimization of modularity.
5. Dynamics, time-scales and Communities (2 lectures): Consensus dynamics; Timescale
separation in dynamical systems and networks; Dynamically invariant subspaces and externally equitable partitions
6. Dynamics I: Random walks (2 lectures): Discrete-time random walks on networks; PageRank; Mean first-passage and recurrence times; Respondent-driven sampling; Continous-Time Random Walks
7. Random walks to reveal network structure (2 lectures): Markov stability; Infomap; Walktrap; Core–periphery structure; Similarity measures and kernels
8. Dynamics II: Epidemic processes (2 lectures): Models of epidemic processes; Mean-Field Theories and Pair Approximations