Things that we always want to know about a graph. Usually:
Number of nodes
Number of edges
For a connectome, maybe number of actual synapses
Density (ER)
compute the density (p) for each connectome, can simply plot each.
Left/right (SBM/DCSBM)
Test different hypotheses about $\hat{B}$ (see statistical connectomics)
is it more densely connected within block than between? To what extent?
maybe can compare this for many of the connectomes. probably not all
core-periphery
etc.
Left/right + any known metadata (SBM/DCSBM)
If any putative cell types are known, use those
now we get a more refined SBM than the above, maybe interesting, maybe not?
cell type data may not be available for all of the above
can do similar tests, results may or may not be different
General low rank (RDPG)
Scree plots
estimation of rank (ZG2)
not sure that this will be interesting to compare across connectome or not. would
have to normalize for the number of nodes somehow, i'd think.
Distribution of weights, degrees
Can just look at distribution of edge weight for each, i guess where weight is number of synapses
in/out degree distribution, marginals and joint, is easy enough to plot.
again, don't know whether it'll be meaningful to compare across connectome or not
More complicated a priori models
Homotypic affinity
can test for whether cell pairs (or blocks?) are more likely than chance to connect (homotypic affinity)
requires having cell pairs
probably only maggot and c. elegans
Testing left vs right, quantify correlation, spectral similarity, GM performance, etc.
Testing for gaia's directedness (or just quantifying to what extent it happens)
degree of reciprocal feedback? had thought about something along the lines of testing
for the difference between left and right latent positions. but maybe a simpler first
statistic to compute is: P(edge from j to i | edge from i to j)
A posteriori models
Spectral clustering and estimating an SBM, DCSBM, DDSBM
can try to incorporate homotypic affinity also... or correlation L/R
figure 3 from maggot paper
Feedforward layout and proportion of feedforward edges
Models with biological metadata
Testing for Peter's rule via the contact graph
is the adjacency a noisy version of the contact graph?
how does rank change as we jitter xyz of synapses
could we also just swap synapses in an epsilon ball and see how structure changes?
Spectral clustering that uses morphology
Configuration models that swap synapses within an epsilon ball
Can we cluster edges via connectivity + space?
had talked about trying to cluster the line graph
spectral embedding of the line graph looked bad when I tried it. Need to follow up.
Niche models that may not work for all data
Different hypotheses for a multilayer SBM-like model
maggot data
Matching FAFB and hemibrain or either to maggot
could be spectral, could be GM
results maybe bad?
could use morphology, could not
Spectral coarsening between maggot and adult
About
Connectocross: statistical characterizations and comparisons of nanoscale connectomes across taxa (A paper in progress)