The Geography of the Mathematics Research Collaboration Graph.

Social networks have become a hot topic for research in the last decade or so. I study one such network in considerable detail: the graph of research collaborations among mathematicians. This graph displays many of the characteristics that various authors have found common to social networks in general. My 'geographical' analysis includes the size of this graph, the distribution of the degrees of its vertices, its connectivity, the distances between its vertices, and its clustering coefficient. I also discuss the playful concept of Erdős numbers. [ABSTRACT FROM AUTHOR]