Improving Power of 2-Sample Random Graph Tests with Applications in Connectomics
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In many applications, there is an interest in testing whether two graphs come from the same distribution, but due to the nature of the data, classic statistical methods are not directly applicable. When the distribution of the two graphs depends on a set of vertex latent positions, in particular under the random dot product graph model, a statistical test is derived by determining whether the set of latent positions are equally distributed. We empirically analyze several methods for this problem, and show that adapting multiscale graph correlation (MGC) to answer this question results in an equivalent test which outperforms several existing methods. We then demonstrate that on a real brain network, MGC is able to detect differences between two sides of a larval Drosophila brain network, whereas other methods fail to detect a difference.
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