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We've a fun new pre-print on how to find out if there is "interesting" structure in your network
AKA finding out if and how your data network departs from your specified null model
(With @jacaballeroo @mathewe @simaggi1 Abhinav Singh)
Thread...
https://arxiv.org/abs/1901.04747
1/ We use a spectral approach: we estimate the distribution of eigenvalues expected under the null model (using generative models), and compare that to the distribution in the actual data network Data eigenvalues exceeding the predicted null model bounds = "interesting"pic.twitter.com/GO4WZDdLke
2/ The corresponding bound-exceeding eigenvectors give us a handy low-dimensional representation of the data network, allowing us to do two things: (i) find the "interesting" structure, by clustering (colours) (ii) reject nodes not contributing to the interesting structure (grey)pic.twitter.com/qOmeZsqXoS
3/ We show this works well on a range of synthetic networks with planted modules: * correctly rejects synthetic networks without modules * correctly finds the modules * even does well at pulling hidden modules out of noise
4/ Applied to real data, we show conclusions about the structure present in a real network can dramatically depend on: (i) whether or not we apply our spectral rejection approach before further analysis (ii) the choice of null model itself
5/ On the Allen Mouse Brain atlas of gene expression, our spectral rejection approach does a lovely job of clustering 625 voxels of gene expression into just 5 meaningful divisions of the entire brainpic.twitter.com/kgVhuou5ym
6/ and when we analyse the dialogue networks of Star Wars Episodes 1-6, we find the prequels have a strongly modular narrative structure, almost as though they were written by a robot... /Finpic.twitter.com/gtb5BeD4r3
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