Není hvězda jako hvězda: identifikace klíčových aktérů v sociálních sítích

Nové přístupy v metodologii sociálněvědního výzkumu


The concept of centrality and centrality measures are well-known and frequently used in social network analysis. They are also implemented in numerous software packages. However, that does not mean that it is easy to apply them correctly. This paper aims to introduce the most frequently used centrality measures, but more importantly to point out the problems related to their application and to sketch potential solutions for these problems. First, three basic centrality measures are introduced: degree, betweenness, and closeness. There are three broad categories of issues with centrality measures. These categories are: inadequate operationalisation of centrality measures, explanation of their distribution, and interdependence of observation in statistical modelling. A typology of flows in the network is presented as a potential solution allowing for transparent operationalisation. The so-called positional approach is another potential solution allowing for conceptually and computationally rigorous definition of centrality measures. Lastly, statistical models for network data are introduced as a way to deal with interdependence of observations. In the conclusion, challenges for measuring centrality in bipartite and multiplex networks are discussed.

Klíčová slova:
social network analysis; centrality measures; methodology

BARABÁSI, Albert-László. 2005. V pavučině sítí. Praha: Paseka.

BARABÁSI, Albert-László a Réka ALBERT. 1999. „Emergence of Scaling in Random Networks.“ Science 286(5439): 509–512.

BATAGELJ, Vladimir a Andrej MRVAR. 1996. Pajek—Program for Large Network Analysis (

BATTISTON, Federico, Vincenzo NICOSIA a Vito LATORA. 2014. „Structural Measures for Multiplex Networks.“ Physical Review E 89: 032804.

BENJAMIN, Daniel. J., James O. BERGER., Magnus JOHANESSON a kol. 2017. „Redefine Statistical Significance.“ Nature Human Behaviour 2: 6–10 (

BLAU, Peter M. 1977. „A Macrosociological Theory of Social Structure.“ American Journal of Sociology 83(1): 26–54.

BORGATTI, Stephen P. 2005. „Centrality and Network Flow.“ Social Networks 27(1): 55–71.

BORGATTI, Stephen P. a Martin G. EVERETT. 1997. „Network Analysis of 2-Mode Data.“ Social Networks 19(3): 243–269.

BORGATTI, Stephen P. a Martin G. EVERETT. 2006. „A Graph-Theoretic Perspective on Centrality.“ Social Networks 28(4): 466–484.

BORGATTI, Stephen P., Martin G. EVERETT a Linton C. FREEMAN. 2002. UCINET 6 for Windows: Software for Social Network Analysis. Analytic Technologies.

BORGATTI, Stephen P., Martin G. EVERETT a Jeffrey. C. JOHNSON. 2013. Analyzing Social Networks. SAGE publications.

BRANDES, Ulrik. 2016. „Network Positions.“ Methodological Innovations 9: 2059799116630650.

BRANDES, Ulrik, Garry L. ROBINS, Anne McCRANIE a Stanley WASSERMAN. 2013. „What is Network Science?“ Network Science 1(1): 1–15.

BROIDO, Anna D. a Aaron CLAUSET. 2019. „Scale-free Networks are Rare.“ Nature Communications 10: 1017.

CAMERER, Colin F., Anna DREBER, Felix HOLZMEISTER a kol. 2018. „Evaluating the Replicability of Social Science Experiments in Nature and Science between 2010 and 2015.“ Nature Human Behaviour 2(9): 637–644.

CASTELLS, Manuel. 2009. The Rise of the Network Society, 2nd edition. Wiley-Blackwell.

CÍSAŘ, Ondřej a Jiří NAVRÁTIL. 2015. „Promoting Competition or Cooperation? The Impact of EU Funding on Czech Advocacy Organizations.“ Democratization 22(3): 536–559.

CLAUSET, Aaron, Cosma R. SHALIZI a Mark E. J. NEWMAN. 2009. „Power-Law Distributions in Empirical Data.“ SIAM Review 51(4): 661–703.

CSARDI, Gábor a Tamasz NEPUSZ. 2006. The Igraph Software Package for Complex Network Research. Cit. 30 dubna 2021 (

DAŇKOVÁ, Hana, Josef BERNARD a Petr VAŠÁT. 2019. „Using the Respondent-Driven Sampling Method to Survey Homeless Populations: Basic Principles, Application and Practical Recommendations.“ Czech Sociological Review 55(2): 189–214.

DE SOLLA PRICE, Derek. 1976. „A General Theory of Bibliometric and Other Cumulative Advantage Processes.“ Journal of the American Society for Information Science 27(5): 292–306.

DIVIÁK, Tomáš 2017. „Equivalence and Blockmodeling in the Analysis of Social Networks.“ Naše společnost 15(1): 27–40.

DIVIÁK, Tomáš, Jan K. DIJKSTRA a Tom A. B. SNIJDERS. 2018. „Structure, Multiplexity, and Centrality in a Corruption Network: The Czech Rath Affair.“ Trends in Organized Crime 22: 274–297.

DIVIÁK, Tomáš, Jan K. DIJKSTRA a Tom A. B. SNIJDERS. 2019. „Poisonous Connections: A Case Study on a Czech Counterfeit Alcohol Distribution Network.“ Global Crime 21(1): 51–73.

EVERETT, Martin. G. 2016. „Centrality and the Dual-Projection Approach for Two-Mode Social Network Data.“ Methodological Innovations 9: 2059799116630662.

EVERETT, Martin G. a Stephen. P. BORGATTI. 2013. „The Dual-Projection Approach for Two-Mode Networks.“ Social Networks 35(2): 204–210.

FREEMAN, Linton C. 1979. „Centrality in Social Networks Conceptual Clarification.“ Social Networks 1(3): 215–239.

FREEMAN, Linton C., Stephen P. BORGATTIA a D. R. WHITE. 1991. „Centrality in Valued Graphs: A Measure of Betweenness Based on Network Flow.“ Social Networks 13(2): 141–154.

GOOD, Phillip I. 2005. Permutation, Parametric and Bootstrap Tests of Hypotheses, 3rd ed. Springer.

HANDCOCK, Mark S., David R. HUNTER, Carter T. BUTTS, Steven M. GOODREAU a Martina MORRIS. 2003. Statnet: Software Tools for the Statistical Modeling of Network Data (

HANNEMAN, Robert a Mark RIDDLE. 2005. Introduction to Social Network Methods. Cit. 5. března 2021 (

KIVELÄ, Mikko, Alex ARENA, Marc BARTHELEMY, James P. GLEESON, Yamir MORENO a Mason A. PORTER. 2014. „Multilayer Networks.“ Journal of Complex Networks 2(3): 203–271.

KLOBUŠIAKOVÁ, Patrícia, Radek MAREČEK, Jan FOUSEK, Eva VÝTVAROVÁ a Irena REKTOROVÁ. 2019. „Connectivity Between Brain Networks Dynamically Reflects Cognitive Status of Parkinson’s Disease: A Longitudinal Study.“ Journal of Alzheimer’s Disease 67(3): 971–984.

LANDHERR, Andrea, Bettina FRIEDL a Julia HEIDEMANN. 2010. „A Critical Review of Centrality Measures in Social Networks.“ Business and Information Systems Engineering, 2(6): 371–385.

LATOUR, Bruno. 2007. Reassembling the Social: An Introduction to Actor-Network-Theory, 1st edition. Oxford University Press.

LUKE, Douglas. A. a J. K. HARRIS. 2007. „Network Analysis in Public Health: History, Methods, and Applications.“ Annual Review of Public Health 28(1): 69–93.

LUSHER Dean, Johan KOSKINEN a Garry L. ROBINS (eds.). 2013. Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications. Cambridge University Press.

MAZÁK, Jaromír a Tomáš DIVIÁK. 2018. „Transactional Activism without Transactions: Network Perspective on Anti-Corruption Activism in the Czech Republic.“ Social Movement Studies 17(2): 203–218.

McPHERSON, Miller 1983. „An Ecology of Affiliation.“ American Sociological Review 48(4): 519–532.

MERTON, Robert K. 1968. „The Matthew Effect in Science: The Reward and Communication Systems of Science are Considered.“ Science 159(3810): 56–63.

MORSELLI, Carlo. 2009. Inside Criminal Networks. New York: Springer.

MORSELLI, Carlo. 2010. „Assessing Vulnerable and Strategic Positions in a Criminal Network.“ Journal of Contemporary Criminal Justice 26(4): 382–392.

NUZZO, Regina. 2014. „Scientific Method: Statistical Errors.“ Nature 506(7487): 150–152.

OCELÍK, Petr, Kamila SVOBODOVÁ, Markéta HENDRYCHOVÁ, Lukáš LEHOTSKÝ, Jo-Anne EVERINGHAM, Saleem ALI, Jaroslaw BADERA a Alex LECHNER. 2019. „A Contested Transition toward a Coal-Free Future: Advocacy Coalitions and Coal Policy in the Czech Republic.“ Energy Research a Social Science 58: 101283.

OPEN SCIENCE COLLABORATION. 2015. Estimating the Reproducibility of Psychological Science.“ Science 349(6251): aac4716.

ORTIZ-ARROYO, Daniel. 2010. „Discovering Sets of Key Players in Social Networks.“ Pp. 27–47 in Ajith ABRAHAM, Aboul-Ella HASSANIEN a Václav SNÁŠEL (eds.). Computational Social Network Analysis. London: Springer.

PADGETT, John F. a Christopher K. ANSELL. 1993. „Robust Action and the Rise of the Medici, 1400–1434.“ American Journal of Sociology 98(6): 1259–1319.

PRELL, Christina. 2011. Social Network Analysis, 1st edition. SAGE Publications Ltd.

ROBINS, Garry L. 2013. „A Tutorial on Methods for the Modeling and Analysis of Social Network Data.“ Journal of Mathematical Psychology 57(6): 261–274.

ROBINS, Garry L. 2015. Doing Social Network Research. SAGE Publications.

ROBINS, Garry L., Philippa PATTISON a Peter ELLIOTT. 2001. „Network Models for Social Influence Processes.“ Psychometrika 66(2): 161–189.

ROBINS, Garry L., Philippa PATTISON a Jodie WOOLCOCK. 2005. „Small and Other Worlds: Global Network Structures from Local Processes.“ American Journal of Sociology 110(4):894–936.

SCHOCH, David a Ulrik BRANDES. 2016. „Re-Conceptualizing Centrality in Social Networks.“ European Journal of Applied Mathematics 27(6): 971–985.

SCHOCH, David. 2018. „Centrality without Indices: Partial Rankings and Rank Probabilities in Networks.“ Social Networks 54: 50–60.

SNIJDERS, Tom A. B. 2013. „Network Dynamics.“ Pp. 252–280 in Rafael WITTEK, Tom A. B. SNIJDERS a Victor NEE (eds). The Handbook of Rational Choice Social Research. Stanford Social Sciences, an imprint of Stanford University Press.

SNIJDERS, Tom A. B. a Christian E. G. STEGLICH. 2015. „Representing Micro–Macro Linkages by Actor-based Dynamic Network Models.“ Sociological Methods a Research, 44(2): 222–271.

SNIJDERS, Tom A. B. 2011. „Statistical Models for Social Networks.“ Annual Review of Sociology 37(1): 131–153.

SOUKUP, Petr. 2019. „The Use of Statistical and Substantive Significance in the Czech Social Sciences.“ Czech Sociological Review 55(2): 215–254.

VALENTE, Thomas W. a Patchareeya PUMPUANG. 2007. „Identifying Opinion Leaders to Promote Behavior Change.“ Health Education a Behavior 34(6): 881–896.

VAŠÁT, Petr a Josef BERNARD. 2015. „Formování komunit, nebo sociální integrace? Analýza personálních sítí ukrajinských imigrantů v Plzni.“ Czech Sociological Review, 51(2): 199-226.

WASSERMAN, Stanley a Katherine FAUST. 1994. Social Network Analysis: Methods and Applications, 1st edition. Cambridge: Cambridge University Press.



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