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Zentralitäts- und Prestigemaße

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Handbuch Netzwerkforschung

Zusammenfassung

Zentralitätsmaße sind Indizes für die „Wichtigkeit“ (Wasserman und Faust 1994) oder „Prominenz“ (Knoke und Burt 1983) eines Knotens in einem Graphen bzw. Akteurs in einem sozialen Netzwerk. Allerdings hat sich in der Netzwerkforschung bislang keine allgemein akzeptierte Definition von Zentralität durchgesetzt (Borgatti und Everett 2006), sodass ungefähr so viele Zentralitätsmaße existieren wie es Vorstellungen von der „Wichtigkeit“ eines Akteurs in einem Netzwerk gibt. Eine zusätzliche Heterogenität resultiert aus dem Umstand, dass die Maße auf zwei grundverschiedenen Richtungen basieren: der Graphentheorie und der Matrixalgebra (Freeman 2008).

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5 Literatur

  • Anthonisse, JacM., 1971: The rush in a graph. Amsterdam: Mathematisch Centrum mimeo.

    Google Scholar 

  • Albert, Reka und Alberto-Laszlo Barabási, 2002: Statistical mechanics of complex networks. Reviews of Modern Physics 74: 47–97.

    Article  Google Scholar 

  • Bavelas, Alex, 1948: A mathematical model for group structure. Applied Anthropology 7: 16–30.

    Google Scholar 

  • Bavelas, Alex, 1950: Communication patterns in task oriented groups. Journal of the Acoustical Society of America 22: 271–282.

    Article  Google Scholar 

  • Beauchamp, Murray A., 1965: An improved index of centrality. Behavioral Science 10: 161–163.

    Article  Google Scholar 

  • Bonacich, Phillip, 1972: Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology 2: 113–120.

    Article  Google Scholar 

  • Bonacich, Phillip, 1987: Centrality and power: a family of measures. American Journal of Sociology 92: 1170–1182.

    Article  Google Scholar 

  • Bonacich, Phillip und Paulette Lloyd, 2001: Eigenvector-like measures of centrality for asymmetric relations. Social Networks 23: 191–201.

    Article  Google Scholar 

  • Bonacich, Phillip und Paulette Lloyd, 2004: Calculating status with negative relations. Social Networks 26: 331–338.

    Article  Google Scholar 

  • Borgatti, Stephen P., 2005: Centrality and network flow. Social Networks 27: 55–71.

    Article  Google Scholar 

  • Borgatti, Stephen P., 2006: Identifying sets of key players in a social network. Computational and Mathematical Organization Theory 12: 21–34.

    Article  Google Scholar 

  • Borgatti, Stephen P. und Martin Everett, 2006: A Graph-theoretic perspective on centrality. Social Networks 28: 466–484.

    Article  Google Scholar 

  • Borgatti, Stephen P., Kathleen M. Carley und David Krackhardt, 2006: On the robustness of centrality measures under conditions of imperfect data. Social Networks 28: 124–136.

    Article  Google Scholar 

  • Brandes, Ulrik und Daniel Fleischer, 2005: Centrality measures based on current flow. S. 533–544 in: Volker Diekert und Bruno Durand (Hg.), STACS 2005, LNCS 3404. Berlin-Heidelberg: Springer.

    Google Scholar 

  • Brandes, Ulrik, 2008: On variants of shortest-path betweenness centrality and their generic computation. Social Networks 30: 136–145.

    Article  Google Scholar 

  • Burt, Ronald S., 1982: Towards a structural theory of action. New York: Academic Press.

    Google Scholar 

  • Everett, Martin G. und Stephen P. Borgatti, 1999: The centrality of groups and classes. Journal of Mathematical Sociology 23: 181–201.

    Article  Google Scholar 

  • Everett, Martin G. und Stephen P. Borgatti 2005a: Ego network betweenness. Social Networks 27: 31–38.

    Article  Google Scholar 

  • Everett, Martin G. und Stephen P. Borgatti, 2005b: Extending centrality. S. 57–76 in: Peter J. Carrington, John Scott und Stanley Wassermann (Hg.), Models and methods in social network analysis. Cambridge: Cambridge University Press.

    Google Scholar 

  • Freeman, Linton C., 1977: A set of measures of centrality based on betweenness. Sociometry 40: 35–41.

    Article  Google Scholar 

  • Freeman, Linton C., 1978/79: Centrality in social networks: Conceptual clarification. Social Networks 1: 215–239.

    Google Scholar 

  • Freeman, Linton C., 1980: The gatekeeper, pair-dependency and structural centrality. Quality and Quantity 14: 585–592.

    Article  Google Scholar 

  • Freeman, Linton C., 2008: Going the wrong way on a one-way street: Centrality in Physics and Biology. Journal of Social Structure 9.

    Google Scholar 

  • Freeman, Linton C., Stephen P. Borgatti und Douglas R. White, 1991: Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks 13; 141–154.

    Article  Google Scholar 

  • Freeman, Linton C., Douglas Roeder und Robert R. Mulholland, 1979/80: Centrality in social networks: II. Experimental results. Social Networks 2: 119–141.

    Google Scholar 

  • Friedkin, Noah E., 1991: Theoretical foundations for centrality measures. American Journal of Sociology 96: 1478–1504.

    Article  Google Scholar 

  • Friedkin, Noah E. und Eugene Johnson, 1997: Social positions in influence networks. Social Networks 19: 209–222.

    Article  Google Scholar 

  • Hage, Per und Frank Harary, 1995: Eccentricity and centrality in networks. Social Networks 17: 57–63.

    Article  Google Scholar 

  • Hubbell, Charles H., 1965: An input-output approach to clique identification. Sociometry 28: 377–399.

    Article  Google Scholar 

  • Jansen, Dorothea, 2003: Einführung in die Netzwerkanalyse. 2. Auflage. Opladen: Leske+Budrich.

    Google Scholar 

  • Katz, Leo, 1953: A new status index derived from sociometric analysis. Psychometrika 18: 39–43.

    Article  Google Scholar 

  • Kim, Pan-Jun und Hawoong Jeong, 2007: Reliability of rank order in sampled networks. European Physical Journal 55: 109–114.

    Google Scholar 

  • Knoke, David und Ronald S. Burt, 1983: Prominence. S. 195–222 in: Ronald S. Burt und Michael J. Minor (Hg.), Applied Network Analysis. Newbury Park, CA: Sage: 195–222.

    Google Scholar 

  • Koschützki, Dirk, Katharina A. Lehmann, Leon Peeters, Stefan Richter, Dagmar Tenfelde-Podehl, Oliver Zlotowski, 2005: Centrality Indices. S. 16–61 in: Ulrik Brandes und Thomas Erlebach (Hg.), Network Analysis. Methodological Foundations. Lecture Notes in Computer Science 3418. Berlin-Heidelberg: Springer.

    Google Scholar 

  • Latora, Vito und Massimo Marchiori, 2007: A measure of centrality based on network efficiency. New Journal Physics 9: 188.

    Google Scholar 

  • Mizruchi, Mark S. und Blyden B. Potts, 1998: Centrality and power revisited: actor success in group decision making. Social Networks 20: 353–387.

    Article  Google Scholar 

  • Mutschke, Peter und Anabel Quan-Haase, 2001: Collaboration and Cognitive Structures in Social Science Research Fields: Towards Socio-Cognitive Analysis in Information Systems. Scientometrics 52: 487–502.

    Article  Google Scholar 

  • Mutschke, Peter, 2008: Zentralitätsanomalien und Netzwerkstruktur. Ein Plädoyer für einen „engeren“ Netzwerkbegriff und ein community-orientiertes Zentralitätsmodell. S. 262–272 in: Christian Stegbauer (Hg.), Netzwerkanalyse und Netzwerktheorie. Wiesbaden: VS-Verlag für Sozialwissenschaften.

    Google Scholar 

  • Newman, Mark E. J., 2003: A measure of betweenness centrality based on random walks. arXiv:cond-mat/0309045 (auch erschienen in Social Networks 27 (2005): 39–54.

    Google Scholar 

  • Nieminen, Juhani, 1974: On centrality in a graph. Scandinavian Journal of Psychology 15: 322–336.

    Article  Google Scholar 

  • Noh, Jae Dong und Heiko Rieger, 2004: Random walk on complex networks. Physical Review Letters 92.

    Google Scholar 

  • Sabidussi, Gert, 1966: The centrality index of a graph. Psychometrika 31: 581–603.

    Article  Google Scholar 

  • Sade, Donald S., 1989: Sociometrics of macaca mulatta III: N-path centrality in grooming networks. Social Networks 11: 273–292.

    Article  Google Scholar 

  • Shimbel, Alfonso, 1953: Structural parameters of communication networks. Bulletin of Mathematical Biophysics 15: 501–507.

    Article  Google Scholar 

  • Shannon, Claude E., 1948: A mathematical theory of communication. The Bell System Technical Journal 27: 379–423, 623–656.

    Google Scholar 

  • Shaw, Marvin E., 1954: Group structure and the behavior of individuals in small groups. Journal of Psychology 38: 139–149.

    Article  Google Scholar 

  • Sparrowe, Raymond T., Robert C. Liden, Sandy J. Wayne, und Maria L. Kraimer, 2001: Social networks and the performance of individuals and groups. Academy of Management Journal 44: 316–325.

    Article  Google Scholar 

  • Stephenson, Karen und Marvin Zelen, 1989: Rethinking centrality: methods and examples. Social Networks 11: 1–37.

    Article  Google Scholar 

  • Tam, Tony, 1989: Demarcating the boundaries between self and the social: the anatomy of centrality in social networks. Social Networks 11: 387–401.

    Article  Google Scholar 

  • Trappmann, Mark, Hans J. Hummell und Wolfgang Sodeur, 2005: Strukturanalyse sozialer Netzwerke. Konzepte, Modelle, Methoden. Wiesbaden: VS Verlag für Sozialwissenschaften.

    Google Scholar 

  • Tutzauer, Frank, 2007: Entropy as a measure of centrality in networks characterized by path-transfer flow. Social Networks 29: 249–265.

    Article  Google Scholar 

  • Valente, Thomas W. und Robert K. Foreman, 1998: Integration and radiality: measuring the extent of an individual's connectedness and reachability in a network. Social Networks 20: 89–105.

    Article  Google Scholar 

  • Valente, Thomas W., Kathryn Coronges, Cynthia Lakon und Elizabeth Costenbader, 2008: How correlated are network centrality measures? Connections 28: 16–26.

    Google Scholar 

  • Wasserman, Stanley, Katherine Faust, 1994: Social Network Analysis. Methods and Applications. Structural Analysis in the Social Sciences 8. Cambridge: Cambridge University Press.

    Google Scholar 

  • Watts, Duncan J., 1999: Small Worlds. Princeton: Princeton University Press.

    Google Scholar 

  • White, Douglas R. und Stephen P. Borgatti, 1994: Betweenness centrality measures for directed graphs. Social Networks 16: 335–346.

    Article  Google Scholar 

  • White, Scott und Padhraic Smyth, 2003: Algorithms for estimating relative importance in networks. Proc. 9th ACM SIGKDD Conference, Washington: 266–275.

    Google Scholar 

  • Zemljič, Barbara und Valentina Hlebec, 2005: Reliability of measures of centrality and prominence. Social Networks 27: 73–88.

    Article  Google Scholar 

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Christian Stegbauer Roger Häußling

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Mutschke, P. (2010). Zentralitäts- und Prestigemaße. In: Stegbauer, C., Häußling, R. (eds) Handbuch Netzwerkforschung. VS Verlag für Sozialwissenschaften. https://doi.org/10.1007/978-3-531-92575-2_33

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  • DOI: https://doi.org/10.1007/978-3-531-92575-2_33

  • Publisher Name: VS Verlag für Sozialwissenschaften

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