Axioms for centrality

Internet Mathematics

Volumn 10, Issue 3-4, 2014, Pages 222-262

  Boldi, Paolo ^a   Vigna, Sebastiano ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84923348084     PISSN: 15427951     EISSN: None     Source Type: Journal    
DOI: 10.1080/15427951.2013.865686     Document Type: Article

References (63)

1. Jac M. Anthonisse. “The Rush in a Graph.” Technical Report, Amsterdam: University of Amsterdam Mathematical Centre, 1971.
2. Alon Altman and Moshe Tennenholtz. “Ranking Systems: The PageRank Axioms.” In Proceedings of the 6th ACM Conference on Electronic Commerce, pp. 1–8. New York, NY: ACM, 2005.
3. Konstantin Avrachenkov and Nelly Litvak. “The Effect of New Links on Google PageRank.” Stochastic Models 22:2 (2006), 319–331.
4. Lars Backstrom, Paolo Boldi, Marco Rosa, Johan Ugander, and Sebastiano Vigna. “Four Degrees of separation.” In ACM Web Science 2012: Conference Proceedings, pp. 45–54. ACM Press, 2012.
5. Alex Bavelas. “Communication Patterns in Task-Oriented Groups.” Journal of Acoustical Socciety of America 22:6 (1950), 725–730.
6. A. Bavelas, D. Barrett, and American Management Association. An Experimental Approach to Organizational Communication. Publications (Massachusetts Institute of Technology. Dept. of Economics and Social Science): Industrial Relations. American Management Association, 1951.
7. Murray A. Beauchamp. “An Improved Index of Centrality.” Behavioral Science 10:2 (1965), 161–163.
8. Claude Berge. Théorie des Graphes et ses Applications. Paris, France:Dunod, 1958.
9. Abraham Berman and Robert J. Plemmons. Nonnegative Matrices in the Mathematical Sciences. Classics in Applied Mathematics. SIAM, 1994.
10. Paolo Boldi, Marco Rosa, and Sebastiano Vigna. “Robustness of Social and Web Graphs to Node Removal.” Social Network Analysis and Mining 3:4 (2013), 829–842.
11. Paolo Boldi, Massimo Santini, and Sebastiano Vigna. “PageRank as a Function of the Damping factor.” In Proc. of the Fourteenth International World Wide Web Conference (WWW 2005), pp. 557–566. Chiba, Japan, 2005. ACM Press, 2005.
12. Paolo Boldi, Massimo Santini, and Sebastiano Vigna. “PageRank: Functional Dependencies.” ACM Trans. Inf. Sys. 27:4 (2009), 1–23.
13. Paolo Boldi and Sebastiano Vigna. “In-Core Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond.” In Proc. of 2013 IEEE 13th International Conference on Data Mining Workshops (ICDMW 2013). IEEE, 2013.
14. Phillip Bonacich. “Factoring and Weighting Approaches to Status Scores and Clique Identification.” Journal of Mathematical Sociology 2:1 (1972), 113–120.
15. Phillip Bonacich. “Simultaneous Group and Individual Centralities.” Social Networks 13:2 (1991), 155–168.
16. Stephen P. Borgatti. “Centrality and Network Flow.” Social Networks 27:1 (2005), 55–71.
17. Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, and Panayiotis Tsaparas. “Link analysis Ranking: Algorithms, Theory, and Experiments.” ACM Transactions on Internet Technology (TOIT) 5:1 (2005), 231–297.
18. Ulrik Brandes, Sven Kosub, and Bobo Nick. “Was messen Zentralitätsindizes?” In Die Integration von Theorie und Methode in der Netzwerkforschung, edited by Marina Hennig and Christian Stegbauer, pp. 33–52. VS Verlag für Sozialwissenschaften, 2012.
19. Alfred Brauer. “Limits for the Characteristic Roots of a Matrix. IV: Applications to Stochastic Matrices.” Duke Math. J. 19:1 (1952), 75–91.
20. Sergey Brin and Lawrence Page. “The Anatomy of a Large-Scale Hypertextual Web Search Engine.” Computer Networks and ISDN Systems 30:1 (1998), 107–117.
21. Robert L. Burgess. “Communication Networks and Behavioral Consequences.” Human Relations 22:2 (1969), 137–159.
22. Steve Chien, Cynthia Dwork, Ravi Kumar, Daniel R. Simon, and D. Sivakumar. “Link Evolution: Analysis and Algorithms.” Internet Math. 1:3 (2004), 277–304.
23. Edith Cohen and Haim Kaplan. “Spatially-Decaying Aggregation over a Network.” Journal of Computer and System Sciences 73:3 (2007), 265–288.
24. Reuven Cohen and Shlomo Havlin. Complex Networks: Structure, Robustness and Function. New York, NY: Cambridge University Press, 2010.
25. B.S. Cohn and M. Marriott. “Networks and Centres of Integration in Indian Civilization.” Journal of Social Research 1:1 (1958), 1–9.
26. Nick Craswell, David Hawking, and Trystan Upstill. “Predicting Fame and Fortune: PageRank or indegree?” In Proceedings of the Australasian Document Computing Symposium, ADCS2003, pp. 31–40, 2003.
27. Gianna Del Corso, Antonio Gullì, and Francesco Romani. “Fast PageRank Computation via a Sparse Linear System.” Internet Math. 2:3 (2006), 251–273.
28. Ayman Farahat, Thomas Lofaro, Joel C. Miller, Gregory Rae, and Lesley A. Ward. “Authority Rankings from HITS, PageRank, and SALSA: Existence, Uniqueness, and Effect of Initialization.” SIAM Journal on Scientific Computing 27:4 (2006), 1181–1201.
29. Linton C. Freeman. “A Set of Measures of Centrality Based on Betweenness.” Sociometry 40:1 (1977), 35–41.
30. L. Freeman. “Centrality in Social Networks: Conceptual Clarification.” Social Networks 1:3 (1979), 215–239.
31. N.E. Friedkin. “Theoretical Foundations for Centrality Measures.” The American Journal of Sociology 96:6 (1991), 1478–1504.
32. Charles H. Hubbell. “An Input-Output Approach to Clique Identification.” Sociometry 28:4 (1965), 377–399.
33. Kalervo Järvelin and Jaana Kekäläinen. “Cumulated Gain-Based Evaluation of IR Techniques.” ACM Trans. Inf. Syst. 20:4 (2002), 422–446.
34. Leo Katz. “A New Status Index Derived from Sociometric Analysis.” Psychometrika 18:1 (1953), 39–43.
35. Maurice G. Kendall. “Further Contributions to the Theory of Paired Comparisons.” Biometrics 11:1 (1955), 43–62.
36. Jon M. Kleinberg. “Authoritative Sources in a Hyperlinked Environment.” Journal of the ACM 46: (1999), 604–632.
37. Donald E. Knuth. “Two Notes on Notation.” American Mathematical Monthly 99:5 (1992), 403–422.
38. H. J. Leavitt. “Some Effects of Certain Communication Patterns on Group Performance.” J. Abnorm. Psychol. 46:1 (1951), 38–50.
39. Ronny Lempel and Shlomo Moran. “SALSA: The Stochastic Approach for Link-Structure Analysis.” ACM Trans. Inf. Syst. 19:2 (2001), 131–160.
40. Ronny Lempel and Shlomo Moran. “Rank-Stability and Rank- Similarity of Link-Based Web Ranking Algorithms in Authority-Connected Graphs.” Information Retrieval 8:2 (2005), 245–264.
41. Lun Li, David L. Alderson, John Doyle, and Walter Willinger. “Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications.” Internet Math. 2:4 (2005), 431–523.
42. Nan Lin. Foundations of Social Research. McGraw-Hill, New York, 1976.
43. Kenneth Mackenzie. “Structural Centrality in Communications Networks.” Psychometrika 31:1 (1966), 17–25.
44. Massimo Marchiori and Vito Latora. “Harmony in the Small-World.” Physica A: Statistical Mechanics and its Applications 285:3–4 (2000), 539–546.
45. J.J. McDonald, M. Neumann, H. Schneider, and M.J. Tsatsomeros. “Inverse m-Matrix Inequalities and Generalized Ultrametric Matrices.” Linear Algebra and its Applications 220 (1995), 321–341.
46. Stanley Milgram. “The Small World Problem.” Psychology Today 2:1 (1967), 60–67.
47. Marc Najork, Sreenivas Gollapudi, and Rina Panigrahy. “Less is More: Sampling the Neighborhood Graph Makes SALSA Better and Faster.” In Proceedings of the Second ACM International Conference on Web Search and Data Mining, pp. 242–251. New York, NY: ACM, 2009.
48. Marc Najork, Hugo Zaragoza, and Michael J. Taylor. “HITS on the Web: How Does it Compare?” In Wessel Kraaij, Arjen P. de Vries, Charles L. A. Clarke, Norbert Fuhr, and Noriko Kando, pp. 471–478. SIGIR 2007: Proceedings of the 30th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. Amsterdam, The Netherlands: New York, NY: ACM, 2007.
49. Marc A. Najork, Hugo Zaragoza, and Michael J. Taylor. HITS on the web: How does it compare? In Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval, SIGIR’07, pages 471–478. ACM, 2007.
50. U.J. Nieminen. “On the Centrality in a Directed Graph.” Social Science Research 2:4 (1973), 371–378.
51. John F. Padgett and Christopher K. Ansell. “Robust Action and the Rise of the Medici, 1400–1434”. The American Journal of Sociology 98:6 (1993), 1259–1319.
52. Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. “The PageRank Citation Ranking: Bringing Order to the Web.” Technical Report SIDL-WP-1999-0120, Stanford Digital Library Technologies Project, Stanford University, 1998.
53. Raj Kumar Pan and Jari Saramäki. “Path Lengths, Correlations, and Centrality in Temporal Networks.” Phys. Rev. E 84:1(2011),016105.
54. Forrest R. Pitts. “A Graph Theoretic Approach to Historical Geography.” The Professional Geographer 17:5 (1965), 15–20.
55. G. Sabidussi. “The Centrality Index of a Graph.” Psychometrika 31:4 (1966), 581–603.
56. John R. Seeley. “The Net of Reciprocal Influence: A Problem in Treating Sociometric Data.” Canadian Journal of Psychology 3:4 (1949), 234–240.
57. Claude E. Shannon. “A Mathematical Theory of Communication.” Bell Syst. Tech. J. 27:3 (1948), 379–423, 623–656.
58. Karen Stephenson and Marvin Zelen. “Rethinking Centrality: Methods and Examples.” Social Networks 11:1 (1989), 1–37.
59. Trystan Upstill, Nick Craswell, and David Hawking. “Query- Independent Evidence in Home Page Finding.” ACM Trans. Inf. Syst. 21:3 (2003), 286–313.
60. René van den Brink and Robert P. Gilles. “A Social Power Index for Hierarchically Structured Populations of Economic Agents.” In Imperfections and Behavior in Economic Organizations, vol. 11 edited by Robert P. Gilles and Pieter H. M. Ruys, pp. 279–318. Netherlands: Springer, 1994.
61. Sebastiano Vigna. “Spectral Ranking.” Preprint, 2009. (http://arxiv.org/abs/0912.0238).
62. Stanley Wasserman and Katherine Faust. Social Network Analysis: Methods and Applications. New York, Cambridge: Cambridge Univ Press, 1994.
63. T.-H. Wei. The Algebraic Foundations of Ranking Theory. PhD thesis, University of Cambridge, 1952.