oeldaghar
commented
5 months ago After experimenting a bit, we more or less found two extremes for hierarchical rewiring.
In the first, we basically bin the edges and perform rewirings within each bin. This is based on the method described in the paper by Sah et al, 2016 ("Exploring community structure in biological networks with random graphs"). However, it is more granular as we explicitly maintain bin-to-bin mixing patterns.
In the second, we cannot partition edges into bins as we have overlapping structure. In this instance we want to preserve the NCP to some extent but by sampling a set for each edge based on the conductance values of sets that touch that edge.
The second can be slow due to edge-to-set queries that could potentially be cached and then updated with edge swaps.
It would be nice to have some comparisons against simple null models for multiscale structure. Some simple ideas are nested SBMs or do something like Louvain, extract the partitions at multiple levels and perform the rewiring in a hierarchical fashion. We've got some code for rewiring but want to be more explicit in how we are performing the subdivision.