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Mapping Knowledge Domains (2004) / Chapter Skim
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Coauthorship networks and patterns of scientific collaboration
Pages 18-23

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From page 18...
... , a number of authors pointed out the potential utility of coauthorship data and in some cases performed small-scale statistical analyses of such things as frequency of coauthored articles by particular authors or authors at particular institutions (3-74. But it was with the advent of comprehensive online bibliographies that construction of complete or near-complete coauthorship networks for entire fields became a realistic possibility.
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From page 19...
... These figures may offer some explanation for the possible lower productivity of mathematics in terms of papers published per unit time: with fewer coauthors Newman Table 1. Summary statistics for the three coauthorship networks analyzed here Biology Number of authors Number of papers Papers per author Authors per paper Average collaborators Largest component Average distance Largest distance Clustering coefficient Assortativity 1,520,251 52,909 2,163,923 98,502 6.4 5.1 3.75 2.53 18.1 9.7 92% 85% 4.6 5.9 24 20 0.066 0.43 0.13 0.36 Physics Mathematics 253,339 6.9 1.45 3.9 82% 7.6 27 0.15 0.12 The statistics are, from top to bottom, total number of authors appearing in the corresponding databases; total number of papers appearing; mean number of papers published by an author; mean number of coauthors on a paper; mean number of different individuals an author collaborated with; largest connected group of individuals in the network; mean vertex-vertex distance between connected individuals in the network; largest such distance; the clustering coefficient, which is the mean probability that two coauthors will also be coauthors of one another; and the degree assortativity coefficient, which is the Pearson correlation coefficient of the degrees (i.e., number of collaborators)
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From page 20...
... Mathematicians have long discussed the "Erdos number," the distance through the mathematics network from a given mathematician to Paul Erdos, an influential Hungarian number theorist of the 20th century who was renowned for his prolific publication and collaboration. Erdos numbers have been studied in depth by a number of authors by using the Mathematical Reviews data (8, 9, 25, 26~.
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From page 21...
... This is the correlation coefficient for the number of collaborators that coauthors have. It lies in the range of -1 to 1, with positive values indicating that people with many collaborators tend to collaborate with others who have many collaborators and negative values indicating the reverse.
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From page 22...
... . I also thank Steve Strogatz for suggesting the "funneling effect" calculation of Statistical Properties of Coauthorship Networks and Laszlo Barabasi, Paul Ginsparg, Jon Kleinberg, Sidney Redner, Steven Strogatz, and Duncan Watts for useful comments and suggestions.
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From page 23...
... Phys. Plasmas Fluids Relat.
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Key Terms

  • betweenness scores
  • mathematical reviews
  • additional results
  • coauthorship network
  • network depicting

  • collaboration patterns
  • paul ginsparg
  • networks studied
  • collaboration networks
  • statistical properties

  • values indicating
  • collaboration strength
  • mathematicians compiled
  • coauthorship data
  • preprint databases

  • scientists tend
  • influential scientists
  • collaboration network
  • clustering coefficient
  • corresponding databases

  • time evolution
  • journal publication
  • particularly paul
  • research accounts
  • include tests

  • assortativity coefficient
  • influential individuals
  • depicting collaborations
  • academic society
  • paper results


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