Theory of Complex Networks (TCN | INK7001U)

Description: The purpose of this module is to provide an appropriate level of understanding of the mathematical theory of complex networks. It will be explained how complex network can be quantified and modelled Syllabus: This course has four parts.

- In part I we focus on the definition and characterization of networks and their topological features. This includes degrees, degree correlations, loops, and spectra.

- In part II we study specific ensembles of random networks, and calculate their properties in the language of part I, such as Erdos-Renyi graphs, small-world networks, `hidden variable' ensembles, and degree-constrained ensembles.

- Part III is devoted to the connection between network topology and collective processes defined on such networks. We discuss the different methods available for studying this link, such equilibrium replica theory, the cavity method, and (very briefly) generating functional analysis.

- In part IV we briefly discuss algorithms for graph generation like preferential attachment, hidden variables, and Steger-Wormald algorithms.

This module is taught at KCL.