Choosing the 'β' Parameter When Using the Bonacich Power Measure


Share / Export Citation / Email / Print / Text size:

Journal of Social Structure

International Network for Social Network Analysis

Subject: Social Sciences


eISSN: 1529-1227





Volume / Issue / page

Volume 22 (2021)
Volume 21 (2020)
Volume 20 (2019)
Volume 19 (2018)
Volume 18 (2017)
Volume 17 (2016)
Volume 16 (2015)
Volume 15 (2014)
Volume 14 (2013)
Volume 13 (2012)
Volume 12 (2011)
Volume 11 (2010)
Volume 10 (2009)
Related articles

VOLUME 12 , ISSUE 1 (December 2011) > List of articles

Choosing the 'β' Parameter When Using the Bonacich Power Measure

Simon Rodan

Keywords : Bonacich power; social network analysis

Citation Information : Journal of Social Structure. Volume 12, Issue 1, Pages 1-23, DOI:

License : (CC BY-NC 4.0)

Published Online: 13-January-2020



Bonacich (1987) suggested a family of centrality measures that provide a useful way of modeling questions of power and network constraint. However, the literature offers little guidance regarding the choice of ß, the parameter which alters the way the measure accounts for the effect of having powerful contacts in ones network. In this paper I explore the way the choice of the ß parameter affects the power indices the Bonacich measure generates. I consider three network properties which might affect the way the choice of ß influences the Bonacich power indices. I find that in high density networks with few internal ‘chains’ and few pendants, the choice of ß is largely immaterial. Conversely, in sparse networks, those with a high proportion of pendant nodes, or those with many chains, the value of ß has a substantial effect on the power indices the measure generates. Next I consider whether power indices produced by interior values of ß might be represented as a linear combination of “pure” vectors, those generated with values of ß at either end of the parameter range and ß = 0. I find that in the vast majority of cases a linear combination of “pure” vectors power is equivalent to using indices produced by interior values of ß, making the choice of ß largely moot. Finally, in the unlikely case that this disaggregation is inappropriate, I discuss the question of determining an appropriate value of ß empirically.

Content not available PDF Share



Backus, J. (1969). The Acoustical Foundations of Music. New York, NY: W.W. Norton.

Bonacich, P. (1987). “Power and Centrality: A Family of Measures Power and Centrality: A Family of Measures.” The American Journal of Sociology 92, 5: 1170-1182.

Borgatti, S.P., M.G. Everett, and L.C. Freeman (2002). UCINET for Windows: Software for Social Network Analysis. Harvard, MA: Analytic Technologies.

Burt, R.S. (1992). Structural Holes: The Social Structure of Competition. Cambridge, MA: Harvard University Press.

Cook, K.S., R.M. Emerson, M.R. Gillmore, and T. Yagamashi (1983). “The Distribution of Power in Exchange Networks: Theory and Experimental Results.” American Journal of Sociology 89, 2: 275-305.

Emerson, R.M. (1962). “Power Dependency Relations.” American Sociological Review 27: 31-40.

Freeman, L.C. (1977). “A Set of Measures of Centrality Based on Betweenness.” Sociometry 40, 1: 35-41.

Perrin, R., T. Charnely, J. DePont (1983). “Normal Modes of the Modern English Church Bell.” Journal of Sound and Vibration 91, 1: 29-49.

Rossing, T.D., and R. Perrin (1987). “Vibration of Bells.” Applied Accoustics 20: 41-70

Watts, D.J. (1999). “Networks, Dynamics, and the Small-World Phenomenon.” The American Journal of Sociology 105, 2: 493-527.

White, H.C. (1992). Identity and Control. Princeton, NJ: Princeton University Press.