Vertex importance
In a graph of friends connected to each other, an interesting question to ask is who the most influential person in the group is. Is it the person with the most connections, that is, the vertex with the highest degree? For directed graphs, in-degree might be a good first guess. Or is it rather the person who knows a selected few people who themselves have a lot of connections? There are certainly many ways to describe how important or authoritative a vertex is and the concrete answer will depend on the problem domain a lot, as well as on what additional data we are given with the graph. Moreover, in the example we have given, for a specific person in the graph another person might be the most influential for their own, very ...
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