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I work with neural networks (ConvNNs, DeepNNs, RNNs/LSTMs) for image segmentation and recognition and Genetic Algorithms for some optimization problems. Recently I started to learn some deep graph theory ideas (random graphs, chromatic numbers, graph coloring). I'm familiar with combinatorics at undergrad level. Are there any existing interesting applications and areas of research of graph theory and combinatorics in ML?

thanks Pablo. Could you give me some links to publications for the 1st and 3rd examples. – Alex – 2016-03-19T12:10:32.913

Take a look to the following slides. There you will see more details about spectral theory and very brief examples of application to shape recognition and webpage ranking (PageRank):

https://www.cs.york.ac.uk/cvpr/talks/PRGraphsFinal.pdf