Features of Collaboration Graphs
By construction, the collaboration graph is a simple graph, since it has no loop-edges and no multiple edges. The collaboration graph need not be connected. Thus people who never co-authored a joint paper represent isolated vertices in the collaboration graph of mathematicians.
Both the collaboration graph of mathematicians and movie actors were shown to have "small world topology": they have a very large number of vertices, most of small degree, that are highly clustered, and a "giant" connected component with small average distances between vertices.
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