Papers of the Regional Science Association

, Volume 7, Issue 1, pp 29–42 | Cite as

A graph theory interpretation of nodal regions

  • John D. Nystuen
  • Michael F. Dacey
Behavioral Models in Regional Analysis


The techniques defined in this paper will divide a set of cities into subgroups which specify a central place and its subordinate hierarchy. The association between cities is not the only system which may be defined as a network of points and lines. Nations or states may be thought of as points with migrations or commodity flows as lines. The important step in the employment of abstract linear graph analysis is the assignment of plausible meaning to the points and lines, preferably in terms of some real world phenomena. The usefulness of the attributes and the interpretation of the resulting hierarchy depends on the correspondence between an empirical example using graph theory analysis and other knowledge of the phenomena. The procedure described in this paper may be employed in a variety of ways, but the application is valid only when significant theoretical conclusions are produced and verified empirically.


Real World Graph Theory Theory Analysis Graph Analysis Central Place 
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  1. 1.
    Berry, B.J.L. and W.L. Garrison, “A Note on Central Place Theory and the Range of a Good,”Economic Geography, Vol. 34 (1958), pp. 304–311. Ullman, E.L., “A Theory for Location of Cities,”American Journal of Socialogy, Vol. 46 (1941), pp. 853–864. Whittlesey D., “The Regional Concept and the Regional Method,”American Geography: Inventory and Prospect, (P.C. James and C.F. Jones, eds.) Syracuse University, Syracuse, 1954.Google Scholar
  2. 2.
    Hammer, C. and F.C. Iklé, “Intercity Telephone and Airline Traffic Related to Distance and the ‘Propensity to Interact‘,”Sociometry, Vol. 20 (1957), pp. 306–316. Harris, C.D.,Salt Lake City: A Regional Capital, University of Chicago, Chicago, 1940. Ullman, E.L.,Mobile: Industrial Seaport and Trade Center, University of Chicago, Chicago, 1940.Google Scholar
  3. 8.
    For example see: Isard, W. and D.J. Ostroff, “General Interregional Equilibrium,”Journal of Regional Science, Vol. 2 (1960) pp. 67–74.Google Scholar
  4. 4.
    Some general statements of graph theory are: König, D.,Theorie der Endlichen und Unenlichen Graphen. Leipzig, 1936 (reprinted by Chelsea Publishing Co., New York, 1950); Berge, C.,Theorie des Graphes et Ses Applications. Dunod, Paris, 1958; Harary, F., “Unsolved Problems in the Enumeration of Graphs,”Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Vol. 5 series A (1960) pp. 63–95;—, “Some Historical and Intuitive Aspects of Graph Theory,”Siam Review Vol. 2 (April 1960) pp. 123–131. The utility of graph theory for geographic analysis has been demonstrated by Garrison, W.L., “Connectivity of the Interstate Highway System,”Papers and Proceeding of The Regional Science Association, Vol. 6 (1960) pp. 121–137.Google Scholar
  5. 5.
    Here, only finite graphs are considered.Google Scholar
  6. 6.
    For examples see, Luce, R.D. and D. Perry, “A Method of Matrix Analysis of Group Structure,”Psychometrika, Vol. 14 (1949) pp. 95–116; and Katz, L., “A New Status Index Derived from Sociometric Analysis,”Psychometrika, Vol. 18 (1953) pp. 39–44.Google Scholar
  7. 7.
    We are indebted to the Pacific Bell Telephone and Telegraph Company and especially to Mr. Homer Moyer, a Seattle officer of that company, for this information.Google Scholar
  8. 8.
    A copy of the entire matrix shown in Table I may be obtained from John D. Nystuen, Department of Geography, University of Michigan.Google Scholar
  9. 9.
    The computations were made possible by a grant of computer time from Western Data Processing, University of California at Los Angeles.Google Scholar
  10. 10.
    Hoover, E.M.,The Location of Economic Activity, McGraw-Hill, New York, 1948. Isard, W.,Location and Space Economy, John Wiley and Sons, New York, 1956. Lösch, A.,The Economics of Location, Yale University, New Haven, 1954.Google Scholar
  11. 11.
    Ullman, E.L.,Growth Centers of the West, University of Washington, Seattle, 1955, p. 48.Google Scholar
  12. 12.
    Hoover, E.M.,op. cit.. Isard, W.,op. cit. Lösch, A.,op. cit. Google Scholar
  13. 13.
    Harary, F., “Status and Contrastatus,”Sociometry, Vol. 22 (1959) pp. 23–43.Google Scholar

Copyright information

© The Regional Science Association 1961

Authors and Affiliations

  • John D. Nystuen
    • 1
    • 2
  • Michael F. Dacey
    • 1
    • 2
  1. 1.University of MichiganUSA
  2. 2.Uuiversity of PennsylvaniaUSA

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