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Co-authorship, rational Erdős numbers, and resistance distances in graphs

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Abstract

The Erdős number (EN) for collaborative papers among mathematicians was defined as indicating the topological distance in the graph depicting the co-authorship relations, i. e., EN = 1 for all co-authors of Paul Erdős; EN = 2 for their co-authors who did not publish jointly with Erdős; etc. A refinement of this notion uses resistance distances leading to rational Erdős numbers (REN), which (as indicated by their name) are rational numbers. For acyclic graphs, EN = REN, but for graphs with circuits these numbers differ. Further refinements are possible using weighted edges in the co-authorship graph according to the number of jointly authored papers.

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References

  1. P. ErdŐs, On the fundamental problem of mathematics. Am. Math. Mon., 79 (1972) 149–150.

    Article  Google Scholar 

  2. C. Goffman, And what is your ErdŐs number ? Am. Math. Mon., 76 (1969) 791.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Harary, The collaboration graph of mathematicians and a conjecture of ErdŐs, J. Rec. Math., 4 (1971) 212–213.

    Google Scholar 

  4. T. Odda, On properties of a well–known graph or what is your Ramsey number ? Ann. N. Y. Acad.. Sci., 328 (1979) 166–172.

    MATH  MathSciNet  Google Scholar 

  5. F. Harary, Graph Theory. Addison–Wesley, Reading, Massachusetts, 1979.

    MATH  Google Scholar 

  6. D. J. Klein, M. Randic, Resistance distance, J. Math. Chem., 12 (1993) 81–95.

    Article  MathSciNet  Google Scholar 

  7. L. W. Shapiro, An electrical lemma. Math. Mag., 60 (1987) 36–38.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. G. Doyle, J. L. Snell, Random Walks and Electrical Networks, Mathematical Association of America, Washington, D.C., 1984.

    Google Scholar 

  9. D. J. Klein, Resistance–distance sum rules, Croat. Chem. Acta, submitted.

  10. D. J. Watts, S. H. Strogatz, Collective dynamics of ‘small–world’ networks, Nature, 393 (1998) 440–442.

    Article  Google Scholar 

  11. D. J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton, 1999.

    Google Scholar 

  12. B. Hayes, Graph theory in practice: Part II. Am. Sci., 88 (2000) 104–109.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Galveston Department of Marine Sciences, Texas A&M University, 5007 Avenue U, Galveston, TX, 77551, USA

    Alexandru T. Balaban & Douglas J. Klein

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  1. Alexandru T. Balaban
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  2. Douglas J. Klein
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Balaban, A.T., Klein, D.J. Co-authorship, rational Erdős numbers, and resistance distances in graphs. Scientometrics 55, 59–70 (2002). https://doi.org/10.1023/A:1016098803527

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