The resulting word2vec model outputs a set of unique skill vectors. The skills that occur in similar contexts (i.e. are often mentioned with the same skills in job adverts) will have similar vectors. We can then compute pairwise cosine similarity scores for all the skill vectors and use these to weight the edges in the skills graph.
Figure \ref{741911} shows a schematic representation of the skills graph, where two skills 'radiology' and 'diagnostic imaging' were mentioned together 1,585 times and the cosine similarity of their word2vec vectors is 0.66. The summary of the steps taken to build the skills graph is provided in Appendix 2 (Figure \ref{768538}).