nodes across OSNs as a *multilayer network* $\cal{M}$, an ensemble of $M$ graphs, each corresponding to an OSN. We indicate the $\alpha$-th layer of the multilayer as $G^\alpha(V^\alpha, E^\alpha)$, where $V^{\alpha}$ and $E^{\alpha}$ are the sets of vertices and edges of the graph $G^{\alpha}$. We can then denote the sequences of graphs composing the $M$-layer multilayer graph as ${\cal{M}} = \{G^1,...,G^\alpha,...,G^M\}$. The graphs are brought together as a multilayer system by the common members across layers as illustrated in Figure \[fig:mdat\].

Multilayer social networks are a natural representation of media multiplexity, as each layer can depict an OSN. Figure \[fig:multi\] illustrates the case at hand, where there are two OSN platforms represented by $G^\alpha$ and $G^\beta$. Members need not be present at all layers and the multilayer network is not limited to two layers. While each platform can be explored separately as a network in its own right, this does not capture the dimensionality of online social life, which spans across multiple OSNs.

[0.24]{} ![Multilayer model of OSNs with [slowromancap1@]{}. Multiplex link; [slowromancap2@]{}. Single-layer link on $G^\alpha$; and [slowromancap3@]{}. Single-layer link on $G^\beta$.[]{data-label="fig:mdat"}](fig1a.pdf "fig:"){width="\textwidth"}

[0.26]{} ![Multilayer model of OSNs with [slowromancap1@]{}. Multiplex link; [slowromancap2@]{}. Single-layer link on $G^\alpha$; and [slowromancap3@]{}. 