I figured out the answer to questions 1 to 3 but I am still having problem
with plotting which I have mentioned in question 4.

Apart from this I am facing another issue.

I had saved my vertex properties which are labels to the vertices in a
variable vprop

print(vprop[i]) will give the node name (in string)

After the minimization of BlockState model, print_summary() gives the brief
info on different layers like this:

stateB.print_summary()  # stateB is the minimized nested block state

l: 0, N: 6525, B: 70
l: 1, N: 70, B: 14
l: 2, N: 14, B: 4
l: 3, N: 4, B: 1
l: 4, N: 1, B: 1


Then levels = stateB.get_levels() gives the blocks in each level and
levels[i] is the individual layers

When I type levels[i].get_blocks() it gives me Property map of key and
corresponding block number in the current level 'i'

Again, levels[i].get_blocks()[12] gives block number.

But How to get the vertex property label/name in subsequent blocks similar
to what I get from vprop ? 





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