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Computing the entropy of a network has proved to be an elusive problem, with potentially enormous impact on the fields of machine learning, complex systems and big data. In this talk I will present an overview of recent work that has shown how ideas from spectral graph theory and statistical physics can be brought to bare on the problem, yielding simple methods for computing network entropy. The topics covered include detecting anomalies in network time series, modelling the time evolution of networks and decomposing networks into frequently occurring substructures, referred to as motifs. I will furnish examples from the financial and medical domains to illustrate the application of these techniques.

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