The graph-tool software allows to define layers for any network where each
layer can have different kinds of interactions of the nodes. It is assumed
that, number of edges are different in each layer but they are between the
nodes which are from a common set.

My question is, after the graph partition has been done to find modules,
does the partition algorithm considers the information from all the layers
to generate a universal partition or it partitions each layer separately ?

Also, if the tool partitions the network by considering the information from
all layers then what edge information it stores finally, given that every
layer had different edge information initially ?

My question is, after the graph partition has been done to find modules,
does the partition algorithm considers the information from all the layers
to generate a universal partition or it partitions each layer separately ?

There are several partition algorithms, so you would need to be more
specific. Both multilayered versions (with edge layers and covariates) yield
a single partition for the whole network. The overlapping versions yield
partitions that can change across layers (as it labels the half-edges,
instead of the nodes). But you can also partition the layers individually by
treating them as separate graphs.

Also, if the tool partitions the network by considering the information from
all layers then what edge information it stores finally, given that every
layer had different edge information initially ?

The clustering algorithm does not change the edges, it only labels the
nodes. It uses the information available in all layers to find the clusters.

I am using "minimize_blockmodel_dl" and "minimize_nested_blockmodel_dl"
functions which can be, as I understand, used as multilayered versions with
edge layers and covariates.