Fast approximation of centrality

Journal of Graph Algorithms and Applications

Volumn 8, Issue 1, 2004, Pages 39-45

  Eppstein, David ^a   Wang, Joseph ^a  

^a Ringgold Standard Institution Informatics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644275245     PISSN: 15261719     EISSN: None     Source Type: Journal    
DOI: 10.7155/jgaa.00081     Document Type: Article

References (28)

1. D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J. Comput., 28(4):1167-1181, 1999.
2. N. Alon, Z. Gali, and O. Margalit. On the exponent of the all pairs shortest path problem. J. Comput. Syst. Sci., 54(2):255-262, April 1997.
3. M. J. Atallah, D. Z. Chen, and D. T. Lee. An optimal algorithm for shortest paths on weighted interval and circular-arc graphs. In Proceedings of First Annual European Symposium on Algorithms, pages 13-24, 1993.
4. A. Bavelas. A mathematical model for group structures. Human Organization, 7:16-30, 1948.
5. A. Bavelas. Communication patterns in task oriented groups. Journal of the Acoustical Society of America, 22:271-282, 1950.
6. M. A. Beauchamp. An improved index of centrality. Behavioral Science, 10:161-163, 1965.
7. P. Bonacich. Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology, 2:113-120, 1972.
8. A. Brandstadt, V. Chepoi, and F. Dragan. The algorithmic use of hypertree structure and maximum neighborhood orderings. In Proceedings of the Graph-Theoretic Concepts in Computer Science, pages 65-80, 1994.
9. D. Z. Chen, D. T. Lee, R. Sridhar, and C. N. Sekharan. Solving the all-pair shortest path query problem on interval and circular-arc graphs. Networks, 31(4):249-257, 1998.
10. C. Cooper, A. Frieze, K. Mehlhorn, and V. Priebe. Average-case complexity of shortest-paths problems in the vertex-potential model. In Proceedings of European Symposium on Algorithms, pages 15-26, 1997.
11. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. J. Symbolic Computation, 9(3):251-280, March 1990.
12. D. Dor, S. Halperin, and U. Zwick. All pairs almost shortest paths. In Proceedings of the 37rd Annual IEEE Symposium on Foundations of Computer Science, pages 452-461, 1996.
13. R. W. Floyd. Algorithm 97: Shortest path. Communication of the Association for Computing Machinery, 5:345, 1962.
14. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal for the Association of Computing Machinery, 34:596-615, 1987.
15. L. C. Freeman. Centrality in social networks: Conceptual clarification. Social Networks, 1:215-239, 1979.
16. N. E. Friedkin. Theoretical foundations of centrality measures. AJS, 96(6):1478-1504, 1991.
17. A. M. Frieze and G. R. Grimmett. The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics, 10:57-77, 1985.
18. K. Han, C. N. Sekharan, and R. Sridhar. Unified all-pairs shortest path algorithms in the chordal hierarchy. Discrete Applied Mathematics, 77:59-71, 1997.
19. W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of American Statistical Association, 58:713-721, 1963.
20. D. B. Johnson. Efficient algorithms for shortest paths in sparse networks. Journal of the Association for Computing Machinery, 24:1-13, 1977.
21. K. Mehlhorn and V. Priebe. On the all-pairs shortest path algorithm of Moffat and Takaoka. In Proceedings of the 3rd Annual European Symposium on Algorithms, pages 185-198, 1995.
22. S. Milgram. The small world problem. Psychol. Today, 2:60-67, 1967.
23. 2 lg n). In Proceedings of the 26th Annual Symposium on Foundations of Computer Science, pages 101-105, 1985.
24. R. Ravi, M. V. Marathe, and C. P. Rangan. An optimal algorithm to solve the all-pair shortest path problem on interval graphs. Networks, 22:21-35, 1992.
25. G. Sabidussi. The centrality index of a graph. Psychometrika, 31:581-603, 1966.
26. R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Syst. Sci., 51(3):400-403, December 1995.
27. D. J. Watts. Small worlds: the dynamics of networks between order and randomness. Princeton University Press, Princeton, N.J., 1999.
28. 2.81 infinite-precision multiplications. Information Processing Letters, 4:155-156, 1976.