Single-layer link on $G^\beta$.[]{data-label="fig:mdat"}](fig1b.pdf "fig:"){width="\textwidth"}

Figure \[fig:links\] illustrates three link types as observed in Figure \[fig:multi\] for the case of a two layer network. Firstly, we define a *multiplex link* between two nodes $i$ and $j$ as a link that exists between them *at least in two layers* $\alpha, \beta \in \cal{M}$. Second, we say that a *single-layer link* between two nodes $i$ and $j$ exists if the link appears *only in one layer* in the multilayer social network. In systems with more layers, multiplexity can take on a value depending on how many layers the link is present on. In the case at hand, given layer $\alpha$ and layer $\beta$, we denote the set of all links present in the multilayer network as $E^{\alpha \cup \beta}$, which yields the global connectivity.

We also define the set of multiplex links as $E^{\alpha \cap \beta}$ and the set of all single-layer links on layer $\alpha$ only as $E^{\alpha \backslash \beta}$. These multilayer edge sets can be further extended to the $M$ layer network by considering more layers $\{1, \dots, M\}$ as part of the intersection or union of graphs. The presence of multiplex and single-layer links in the above edge sets 