defines the multilayer neighbourhood of nodes in the network, as expanded upon next.

The Multilayer Neighbourhood
----------------------------

Following our definition of a multilayer online social network, we can redefine the ego network of a node as the *multilayer neighbourhood*. While the simple node neighbourhood is the collection of nodes one hop away from the ego, the multilayer global neghbourhood (denoted by $GN$) of a node $i$ can be derived by the total number of unique neighbours across layers:

$$\Gamma_{GNi} = \{j \in V^{\cal{M}} : e_{i,j} \in E^{\alpha \cup \beta}\}$$

and their global multilayer degree as:

$$k_{GNi} = | \Gamma_{GNi}|$$

which provides insight into the entire connectivity of nodes across layers, and can therefore be interpreted as a global measure of the immediate degree of a node. We can similarly define the core neighbourhood (denoted by $CN$) of a node $i$ across layers of the multilayer network as:

$$\Gamma_{CNi} = \{j \in V^{\cal{M}} : e_{i,j} \in E^{\alpha \cap \beta}\}$$

and their core multilayer degree as:

$$k_{CNi} = | \Gamma_{CNi}|$$

where we only consider neighbours which exist across all layers. This simple formulation allows for powerful extensions of existing metrics of local neighbourhood similarity. We can define the overlap (Jaccard similarity) of 