Centers in Connected Undirected Graphs: An Axiomatic Approach

References

• Beauchamp M. A. An improved index of centrality. Behavioral Sci. (1965) 10:161–163Crossref, Google Scholar
• Berman A., Plemmons R. J.Nonnegative Matrices in the Mathematical Sciences (1979) (Academic Press, New York) Google Scholar
• Bonacich P. Factoring and weighting approaches to status scores and clique identification. J. Math. Sociology (1972) 2:113–120Crossref, Google Scholar
• Bonacich P. Power and centrality: A family of measures. Amer. J. Sociology (1987) 92:1170–1182Crossref, Google Scholar
• Chebotarev P. Yu., Shamis E. On proximity measures for graph vertices. Automation Remote Control (1998) 59(10):1443–1459Google Scholar
• Clever Project Hypersearching the Web. Sci. Amer. (1999) June):44–52Google Scholar
• Cross R., Prusak L. The people who make organizations go—or stop. Harvard Bus. Rev. (2002) June):104–112Google Scholar
• Delver R., Monsuur H. Stable sets and standards of behaviour. Soc. Choice Welfare (2001) 18(3):555–570Crossref, Google Scholar
• Delver R., Monsuur H., Storcken A. J. A. Ordering pairwise comparison structures. Theory and Decision (1991) 31:75–94Crossref, Google Scholar
• Dutta B., Laslier J.-F. Comparison functions and choice correspondences. Soc. Choice Welfare (1999) 16:513–532Crossref, Google Scholar
• Faust K. Centrality in affiliation networks. Soc. Networks (1997) 19:157–191Crossref, Google Scholar
• Fishburn P. C. Condorcet social choice functions. SIAM J. Appl. Math. (1977) 33:469–489Crossref, Google Scholar
• Foster D., Vohra R. An axiomatic characterization of a class of locations on trees. Oper. Res. (1998) 46:347–354Link, Google Scholar
• Freeman L. C. A set of measures of centrality based on betweenness. Sociometry (1977) 40:35–41Crossref, Google Scholar
• Freeman L. C. Centrality in social networks conceptual clarifications. Soc. Networks (1979) 1:215–239Crossref, Google Scholar
• Friedkin N. E. Theoretical foundations for centrality measures. Amer. J. Sociology (1991) 96:1478–1504Crossref, Google Scholar
• Gulati R., Gargiulo M. Where do inter-organizational networks come from? Amer. J. Sociology (1999) 104(5):1439–1493Crossref, Google Scholar
• Haynes T. W., Hedetniemi S. T., Slater P. J.Fundamentals of Domination in Graphs (1998) (Marcel Dekker, Inc., New York) Google Scholar
• Holzman R. An axiomatic approach to location on networks. Math. Oper. Res. (1990) 15:553–563Link, Google Scholar
• McMorris F. R., Mulder H. M., Powers R. C. The median function on median graphs and semilattices. Discrete Appl. Math. (2000) 101:221–230Crossref, Google Scholar
• Miller N. R. A new solution set for tournament and majority voting: Further graph-theoretical approaches to the theory of voting. Amer. J. Political Sci. (1980) 24:68–96Crossref, Google Scholar
• Moulin H.The Strategy of Social Choice (1983) (North-Holland, Amsterdam, The Netherlands) Crossref, Google Scholar
• Moulin H. Choosing from a tournament. Soc. Choice Welfare (1986) 3:271–291Crossref, Google Scholar
• Papendieck B., Recht P. On maximal entries in the principle eigenvector of graphs. Linear Algebra Appl. (2000) 310:129–138Crossref, Google Scholar
• Richter M. K. Revealed preference theory. Econometrica (1966) 34:635–645Crossref, Google Scholar
• Rubinstein A. Ranking the participants in a tournament. SIAM J. Appl. Math. (1980) 38:108–111Crossref, Google Scholar
• Ruhnau B. Eigenvector centrality a node centrality? Soc. Networks (2000) 22:357–365Crossref, Google Scholar
• Sabidussi G. The centrality index of a graph. Psychometrica (1966) 31:581–603Crossref, Google Scholar
• Seidman S. B. Structural consequences of individual position in nondyadic social networks. J. Math. Psych. (1985) 29:367–386Crossref, Google Scholar
• Shapley L. S., Kuhn H. W., Tucker H. W. A value for n-person games. Contributions to the Theory of Games, Vol. 2, Ann. Math. Stud. 28 (1953) (Princeton University Press, Princeton, NJ) 307–317Crossref, Google Scholar
• Vohra R. An axiomatic characterization of some locations on trees. Eur. J. Oper. Res. (1996) 90:78–84Crossref, Google Scholar
• Wasserman S., Faust K.Social Network Analysis: Methods and Applications (1994) (Cambridge University Press, Cambridge, U.K.) Crossref, Google Scholar
• Wiener H. Structural determination of paraffin boiling points. J. Amer. Chem. Soc. (1947) 69:17–20Crossref, Google Scholar
• Young H. P. Social choice scoring functions. SIAM J. Appl. Math. (1975) 28:824–834Crossref, Google Scholar