Advanced search
Publication Cover
The Journal of Mathematical Sociology Volume 41, 2017 - Issue 3
Submit an article Journal homepage
162
Views
4
CrossRef citations to date
0
Altmetric
Articles

Aggregating nonnegative eigenvectors of the adjacency matrix as a measure of centrality for a directed graph

Neng-Pin LuDepartment of Information Management, Chang Gung University, Kwei-Shan, Tao-Yuan, TaiwanCorrespondence[email protected]
Pages 139-154 | Received 20 Oct 2016, Accepted 07 May 2017, Published online: 07 Jun 2017

References

  • Bapat, R. B. (1998). A max version of the Perron-Frobenius theorem. Linear Algebra and Its Applications, 275, 3–18. doi:10.1016/S0024-3795(97)10057-X
  • Berman, A., & Shaked-Monderer, N. (2012). Non-negative matrices and digraphs. In R. A. Meyers (Ed.), Computational complexity: Theory, techniques, and applications (pp. 2082–2095). New York, NY: Springer.
  • Bonacich, P. (1972). Factoring and weighting approaches to status scores and clique identification. The Journal of Mathematical Sociology, 2(1), 113–120. doi:10.1080/0022250X.1972.9989806
  • Bonacich, P. (1987). Power and centrality: A family of measures. American Journal of Sociology, 92(5), 1170–1182. doi:10.1086/228631
  • Bonacich, P., & Lloyd, P. (2001). Eigenvector-like measures of centrality for asymmetric relations. Social Networks, 23(3), 191–201. doi:10.1016/S0378-8733(01)00038-7
  • Borgatti, S. P. (2002). NetDraw: Graph Visualization Software. Harvard, MA: Analytic Technologies.
  • Brualdi, R. A. (2010). Spectra of digraphs. Linear Algebra and Its Applications, 432(9), 2181–2213. doi:10.1016/j.laa.2009.02.033
  • Chung, F. R. K. (1997). Spectral Graph Theory. Providence, RI: American Mathematical Society.
  • Dasgupta, S., Papadimitriou, C. H., & Vazirani, U. V. (2006). Algorithms. New York, NY: McGraw-Hill.
  • Freeman, L. C. (1979). Centrality in social networks: Conceptual clarification. Social Networks, 1(3), 215–239. doi:10.1016/0378-8733(78)90021-7
  • Freeman, L. C. (2008). Going the wrong way on a one-way street: Centrality in physics and biology. Journal of Social Structure, 9(2).
  • Friedkin, N. E. (1991). Theoretical foundations for centrality measures. American Journal of Sociology, 96(6), 1478–1504. doi:10.1086/229694
  • Gould, R. V. (2002). The origins of status hierarchies: A formal theory and empirical test. American Journal of Sociology, 107(5), 1143–1178. doi:10.1086/341744
  • Hubbell, C. (1965). An input-output approach to clique identification. Sociometry, 28(4), 377–399. doi:10.2307/2785990
  • Katz, L. (1953). A new status index derived from sociometric analysis. Psychometrika, 18(1), 39–43. doi:10.1007/BF02289026
  • Langville, A. N., & Meyer, C. D. (2006). Google’s pagerank and beyond: The science of search engine rankings. Princeton, NJ: Princeton University Press.
  • Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). The pagerank citation ranking: Bringing order to the web. Technical Report. Stanford InfoLab. <http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf>
  • Parlett, B. N., Simon, H., & Stringer, L. M. (1982). On estimating the largest eigenvalue with the Lanczos algorithm. Mathematics of Computation, 38(157), 153–165. doi:10.1090/S0025-5718-1982-0637293-9
  • Richards, W., & Seary, A. (2000). Eigen analysis of networks. Journal of Social Structure, 1(2), 1–17.
  • Sahni, S. (2001). Data structures, algorithms, and applications in java. New York, NY: McGraw-Hill.
  • Seary, A., & Richards, W. (2003). Spectral methods for analyzing and visualizing networks: An introduction. In B. Breiger, K. Carley, & P. Pattison (Eds.), Dynamic social network modeling and analysis: Workshop summary and papers (pp. 209–228). Washington, DC: The National Academies Press.
  • Spielman, D. (2012). Spectral graph theory. In U. Naumann, & O. Schenk (Eds.), Combinatorial scientific computing (pp. 495–524). Boca Raton, FL: CRC Press.
  • Tarjan, R. (1972). Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1(2), 146–160. doi:10.1137/0201010
  • Weeks, M. R., Clair, S., Borgatti, S. P., Radda, K., & Schensul, J. J. (2002). Social networks of drug users in high-risk sites: Finding the connections. AIDS and Behavior, 6(2), 193–206. doi:10.1023/A:1015457400897

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Supercharge Your Next Research Paper: Research and write your next paper with Jenni AI.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.