Structure of multilayer network


I have a question regarding the structure of multilayer networks.

Can we propose a multi-layer network where :

a) A set of nodes are common to all the layers, say common set nodes and
b) every layer has its' own set of nodes, that also interacts with the
common set nodes, which may or may not be present in other layers?

For example:

Layer 1: Nodes: a, b, c, d
Layer 2: Nodes: f, e, c, d
Layer 3: Nodes: e, a, c, d

Here, node 'c' and 'd' are present in all the layers. Each layer has some
nodes which are not common to all the layers but present in at least two
layers. Like nodes, 'a' and 'e'
So, will it be correct to represent such a network using graph tool for SBM

What would define a community in such networks? I tried the same with a toy
network where the final minimized state gives edges and nodes lesser than
the original multigraph network.