Outline

Outline#

In Unmatched vs. matched networks we briefly explain the difference between a matched and an unmatched pair of networks.
In Larval Drosophila melanogaster brain connectome we explain what data we’ll use for our comparisons.

In Density test, we run a test for whether the Erdos-Renyi model fits between the two hemispheres are similar, finding that they are significantly different even under this simple model.
In Group connection test, we run a test for whether stochastic block model fits between the two hemispheres are similar. We also present a version for this test which accounts for differences in edge density between the hemispheres.
In An embedding-based test, we run a test for whether random dot product graph model fits between the two hemispheres are similar. We find that in general, this test fails to reject the null hypothesis of bilateral symmetry, but that this analysis is highly sensitive to the choice of embedding dimension.s
In (COMING SOON), we run each of these tests over perturbed versions of the left and right connectomes to analyze their power under a variety of alternatives to our null hypothesis of symmetry.

In A density-based test, we again test for bilateral symmetry under the Erdos-Renyi model, this time using the matched/known-node-correspondence data. Again, we find that the two hemispheres are significantly different under this model.
In A group-based test, we perform a test for stochastick block model fit symmetry using the matched data. Again, we find that the stochastic block model fits are significantly different, but when adjusting to correct for a difference in density, this difference disappears.

An exact test for non-unity null odds ratios describes a modified Fisher’s exact test, supporting some of the work in .
(COMING SOON) closely examines the effect of embedding dimension on the test presented in An embedding-based test, demonstrating that artificially low p-values can be the result of misaligned network embeddings caused by close eigenvalues. This highlights the importance of carefully examining the embeddings and spectra when comparing networks with this method, and also that overshooting the embedding dimension can be helpful to avoid this problem.