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Proximity from a graph perspective can be interpreted in different ways.
For example (and maybe more prominent) it can be the graph distance between nodes (geodesic distance or length of shortest path connecting two nodes), which would literally tell you how close two nodes are in the graph. Other variants can be used as well, like length of a random walk between them.
Also, it could mean the similarity of two nodes with respect to some attributes attached to them, so similarity in a N-dimensional attribute space: similarity in centrality scores, ego-neighborhoods or communities, clustering, etc.
Hope this gives you some ideas to start searching for appropriate references on the web.