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In mathematics and social science, a collaboration graph〔Frank Harary. ''Topics in Graph Theory''. New York Academy of Sciences, 1979. ISBN 0-89766-028-5〕 is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network. ==Types of collaboration graphs considered in the literature== The most well-studied collaboration graphs include: *Collaboration graph of mathematicians also known as the Erdős collaboration graph,〔Vladimir Batagelj and Andrej Mrvar, (''Some analyses of Erdos collaboration graph.'' ) Social Networks, vol. 22 (2000), no. 2, pp. 173–186.〕〔Casper Goffman. ''And what is your Erdos number?'', American Mathematical Monthly, vol. 76 (1979), p. 791〕 where two mathematicians are joined by an edge whenever they co-authored a paper together (with possibly other co-authors present). *Collaboration graph of movie actors, also known as the Hollywood graph or co-stardom network,〔Chaomei Chen, C. Chen. ''Mapping Scientific Frontiers: The Quest for Knowledge Visualization.'' Springer-Verlag New York. January 2003. ISBN 978-1-85233-494-9. See p. 94.〕〔Fan Chung, Linyuan Lu. ''Complex Graphs and Networks, Vol. 107.'' American Mathematical Society. October 2006. ISBN 978-0-8218-3657-6. See p. 16〕〔Albert-László Barabási and Réka Albert, (''Emergence of scaling in random networks.'' ) Science, vol. 286 (1999), no. 5439, pp. 509–512〕 where two movie actors are joined by an edge whenever they appeared in a movie together. *Collaborations graphs in other social networks, such as sports, including the "NBA graph" whose vertices are players where two players are joined by an edge if they have ever played together on the same team.〔V. Boginski, S. Butenko, P.M. Pardalos, O. Prokopyev. ''Collaboration networks in sports''. pp. 265–277. Economics, Management, and Optimization in Sports. Springer-Verlag, New York, February 2004. ISBN 978-3-540-20712-2〕 *Co-authorship graphs in published articles, where individual nodes may be assigned either at the level of the author, institution, or country. These types of graphs are useful in establishing and evaluating research networks. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Collaboration graph」の詳細全文を読む スポンサード リンク
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