Network Science is a now well-established field of research at the intersection of mathematics, statistics, physics and computer science. Networks can be used to represent systems ranging from news and social networks (such as Twitter, Facebook, Google+ or school interaction networks) to physical systems (such as gene interactions networks, gas or electric networks). This module will provide students with a well-rounded understanding in the application of network science methods to the range of areas listed above. To accomplish this we will cover 1) network structure and properties, 2) results from ensembles of random networks, 3) methods for estimating latent properties of networks, such as community structure and 4) how networks can be used to model dynamical processes (such as the spread of contagions). These will be taught with an emphasis on theoretical results and real-world modelling.

Develop an understanding of how the patterns of connections in large systems (the network structure) affect the behaviour of the system (the dynamics), and how to apply algorithms to analyse network-based relationships in data. 1. Introduction to the large-scale structure of networks: components, shortest paths and the small world effect, degree distributions, power laws and scale free networks, clustering coefficients, multilayer networks. 2. Measures and metrics for network structure: centrality, PageRank, transitivity, assortativity. 3. Matrix algorithms for large networks: spectral methods, partitioning, community detection. 4. Dynamical systems on networks: percolation, biological contagions (epidemics), social contagions and information diffusion. 5. Simulation methods for dynamics on networks: Monte Carlo simulation. Dynamically evolving networks.

Upon successful completion of this module, students will be able to: 1. Illustrate the role of complex networks as representations of real-world systems. 2. Reproduce theoretical results from network science and compare to real-world data. 3. Define and estimate the properties of a network's structure. 4. Use matrix algorithms to infer, if present, the community structure of a network. 5. Set up Monte-Carlo simulation schemes to relate simulation results to network theory results. 6. Contrast the impact of a network's structural properties on different types of dynamical processes (such as the spread of epidemics or the robustness of the network).

Upon successful completion of this module, students will be able to: 1. Demonstrate an appreciation of the versatility of networks for representing a variety of complex systems. 2. Interrogate and justify the mathematical assumptions of a wide range of network models and recognise the limitations of their validity. 3. Show an awareness of the importance of network structure effects on dynamics (e.g., the effect of clustering on epidemic spread).

N/A

This module will use the normal lecture and tutorial mode of delivery. Lectures will be used to deliver the main theoretical content. Tutorials will be used to apply theory learned in lectures to problem sets. Additionally, students will be given the opportunity to work through problem sets in groups. The computer laboratories will supplement content from lectures and tutorials with hands-on implementation of the network concept, such as community detection, with large synthetic and real-world datasets. New development in network science will be introduced via guest lectures. This will expose the students to the state of the art in the field. This framework for teaching will allow the following graduate attributes to be instilled in the student by the end of the module: 1) KNOWLEDGEABLE: Student will have learned not only theoretical network science results but how to implement these in real-world settings. 2) COLLABORATION and ARTICULATE: Students during the tutorial and lab-based sessions will work in small groups. This aids in the development of soft skills such as the ability to work in teams with their peers and communicate possible issues and solutions to a given problem. 3) CREATIVE: Application of network theory will not mean a direct, easy, implementation of a method to a real-world problem that students will encounter in the labs. Here the students will build an ability to identify the salient parts of a method and create their own implementation for the real-world problem at hand. In addition to this, the guest lecturers will provide students with exposure to how researchers creatively solve problems to create the current state of the art methods. 4) PROACTIVE and RESPONSIBLE: Student will have to take initiative in managing required reading material, their problem set submissions and their lab-based assignments.