The heterogeneous inter-relations between the components of complex systems are frequently represented via graphs or networks; examples range from protein-protein interactions in biology, over social networks connecting human beings up to large-scale technological networks like the internet or power grids. A huge variety of methods have been developed over the last years to reconstruct networks from observational data, to analyse a network’s structure, or to understand its implications on processes taking place on top of these networks. Many of these methods have been inspired by the statistical physics of disordered systems. My lecture series will cover four major topics:
(i) models of networks (random graphs, small-world networks, scale-free networks, network ensembles),
(ii) characterisation of networks (degree distribution, centrality measures, k-core, community detection),
(iii) models on networks (Ising model, optimisation over networks, epidemic spreading models),
(iv) inference of networks (correlation networks, Gaussian networks, inverse statistical physics).
The focus of the course will be to give a solid and coherent methodological and theoretical basis, which can be used across a broad range of applications.