Centers in connected undirected graphs: An axiomatic approach

Operations Research

Volumn 52, Issue 1, 2004, Pages 54-64

  Monsuur, Herman ^a   Storcken, Ton ^b  

^a Royal Netherlands Naval College   (Netherlands)

^b MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

Axiomatic approach; Networks graphs: centrality; Social networks

Indexed keywords

COMMERCE; COMPUTATIONAL COMPLEXITY; MATHEMATICAL MODELS; PROBLEM SOLVING; SET THEORY;

AXIOMATIC APPROACH; NETWORKS/GRAPHS; SOCIAL NETWORKS;

GRAPH THEORY;

EID: 10844273315     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.1030.0082     Document Type: Article

References (34)

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