Module Directory

Network theory is an active and dynamic area of research with applications across many fields, as such developments in the theory have appeared rapidly in recent years. The interdisciplinary nature of the topic has led to applications in biology, neurology, psychology, physical systems (such as power grids, transportation or communication systems), computer science, social sciences and economic theory.

This module is an introduction to networks and to their analysis. Starting from the initial description of networks, it leads to studying their mathematical properties and describing how such properties arise in real-world applications. Algorithms used to determine such properties and structures will be introduced and explored. Leading to an understanding of what network analyses can tell us about data sets.

The aims of this module are:

• To introduce students to the concept of a network along with descriptions of the most common types of networks, learning how and why they appear in various real-world systems.


• To develop an understanding of some of the common properties of networks such as centrality, connectedness and clustering and learn how to detect these structures.


• To introduce and discuss algorithms used to determine properties and will allow students to analyse complex network data, with the programming skills developed allowing them to visualise and present their findings in a clear manner.

By the end of this module, students will be expected to be able to:

1. Implement algorithms for network analysis using Python and networkX.


2. Calculate and interpret key features and properties of networks.


3. Have a systemic understanding of network structures and how to estimate these based on modelled and empirical data.


4. Develop an understanding of how networks can be used to model complex systems from various disciplines, identifying the characteristics of systems which indicate such an analysis is appropriate.


5. Critically analyse network datasets and interpret results.


6. Understand algorithms used to determine properties and structures of networks and have a critical awareness as to when they are appropriate to use.


7. Understand group/community structure of networks


8. Communicate the results of technical analyses in a clear manner.

Syllabus

• Introduction to network analysis using Python and networkX – basic commands for creating, importing, manipulating, analysing, and visualizing networks.


• Introduction to basic network theory: basic definition of a network; directed/undirected network; closed/open paths; cliques; common types of graph (bipartite, connected, cyclic etc.)


• Common structures used in network theory: the notion of centrality and the various versions of centrality (e.g. degree, closeness, betweenness); degree distribution; modularity; network density; clustering/communities.


• Common types of networks and methods of constructing/identifying such networks and how these arise in real-world settings, including: random networks (e.g. Erdos-Renyi networks); small-world networks (e.g. Watts-Strogatz networks); scale-free networks (e.g. Barabasi networks).


• Common algorithms used to determine properties and structures of networks and the implications of these properties on real-world processes: breadth-first search/width-first search; clustering/community detection.

Teaching in the department will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.