Undirected edge inference -- some failure modes

I considered the undirected edge inference task for higher edge densities. My "standard" model currently uses $M=100$, $N=100$, which is a very sparsely connected ($1\%$) network. I considered how the difficulty of the task varies for $M=500$, $M=1000$.

At $M=500$, the inference run finds many more edges than the true number. I think that the cross-correlation does not have the means to distinguish between direct and complex descendant relationships, and that it will tend to close triads. It seems to me that Granger causality would better handle dense graphs (since G-causality asks whether $X_1$ influences $X_2$ when other $\left\{X_i\right\}$ are given).

At $M=1000$, the Izhikevich model itself "locks up," and all spikes become "phase-locked." It appears that the coupling coefficient $\alpha$ that I am using is too high to support such a dense network.

These observations suggest that I should consider a case with lower $\alpha$, as to explore varying edge densities in the inference.

It also suggests to me to try out bipartite populations of neurons with dominant synaptic connections between the parts. This actually models the kind of experiments that I want to eventually undertake.