On page 4 of [1 ] , you find:

> [...] a *multiplex network* can be represented as a collection of graphs
$$\mathcal{G}=\{G^{(\ell)}=(V_n,E^{(\ell)})\}_{\ell \in V_L}$$
where $V_n=\{1,\ldots,n\}$ is the set of nodes, $V_l=\{1,\ldots,L\}$ s the set of layers and $E^{(\ell)}\subset V_n\times V_n$ is the set of edges on layer $\ell$. 

These structures are also sometimes called *multi-layer graphs*. Note that in the above formulation it is assumed that the nodes on each layer are the same (this models the bijective edges you are referring to).


[1 ] *Node and layer eigenvector centralities for multiplex networks.*
F Tudisco, F Arrigo, A Gautier - SIAM Journal on Applied Mathematics, 2018
([arXiv][1])


  [1]: https://arxiv.org/pdf/1711.08448.pdf