two users $i$ and $j$’s global neighbourhoods as:

$$sim_{GNij} = \frac{|\Gamma_{GNi} \bigcap \Gamma_{GNj}|}{|\Gamma_{GNi} \bigcup \Gamma_{GNj}|}$$

where the number of common friends is divided by the number of total friends of $i$ and $j$. The same can be done for the core degree of two users. The Jaccard coefficient, often used in information retrieval, has also been widely used in link prediction [@liben2007link].

We can further extend our definition of the multilayer neighbourhood to the Adamic/Adar coefficient for link likelihood [@adamic2001], which considers the overlap of two neighbourhoods based on the popularity of common friends (originally through web pages) in a single-layer network as:

$$aa\_sim_{GNij} = \sum_{z \in \Gamma_{GNi} \bigcap \Gamma_{GNj}} 
    \frac{1}{log(|\Gamma_{GNz}|)}$$

where it is applied to the global common neighbours between two nodes but can be equally applied to their core neighbourhoods. This metric has shown to be successful in the link prediction in its original single-layer form in both social networks and location-based networks [@liben2007link; @scellato2011exploiting]. In the present work, we aim to show its applicability to the multilayer space in predicting online social links across and between Twitter and Foursquare. We will next describe the specific datasets, which we apply this framework to.

Dataset
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Twitter and Foursquare 