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Network Centrality and Power

centpowfilename,[normalizebeta(real)saveas(filename)]

Description

centpowcreates a new dataset containing the degree centrality, alter-based centrality and power, and beta centrality and power for each node in a symmetric network described byfilename. [NOTE: This command does not affect the data in memory.]

OptionsnormalizeRequests that each measure be normalized using the approach described by Bonacich (1987).beta(real)Specifies the value of thebetaparameter used to compute beta centrality and power (must be positive). [Default = .995 * 1/largest eigenvalue; this makes beta centrality roughly equivalent to eigenvector centrality.]saveas(filename)Specifies the name of the new file containing the centrality and power scores. The default iscentpow.dta.

Inputfilenamemust be a comma-delimited file containing a square, symmetric matrix. The matrix entries may be either binary or valued.

Each vector of scores is saved as a variable, with the observations in the same order as the rows and columns of the input matrix.OutputDegree centrality is defined as a node's total number of connections, and is saved as the variable

degree.Alter-based centrality and power are extensions of degree centrality in which each node's score is based on the degree centrality of the nodes to which it is connected. Alter-based centrality is defined as the sum of the degree centralities of a node's alters, and is saved as the variable

altercent. Alter-based power is defined as the sum of the inverse degree centralities of a node's alters, and is saved as the variablealterpow.Beta centrality and power are saved as the variables

betacentandbetapow, respectively. These measures are conceptually similar to alter-based centrality and power, and often yield similar results. However, they are computationally distinct (see Bonacich 1987) and are subject to several assumptions:(1) The network contains no disconnected components,

(2) The largest eigenvalue is substantially larger than the 2nd largest eigenvalue,

(3) The absolute value of

betais less than the reciprocal of the largest eigenvalue.If any of these assumptions is violated, the command will issue a warning, but will still compute the measures.

ReferencesNeal, Z. P. (2011) Differentiating Centrality and Power in the World City Network,

Urban Studies48: 2733-2748. (CLICK FOR PDF)Neal, J. W. and Z. P. Neal. (in press) Power as a Structural Phenomenon,

American Journal of Community Psychology48: 157-167. (CLICK FOR PDF)Bonacich, P. (1987) Power and Centrality: A Family of Measures,

AmericanJournal of Sociology92: 1070-82.

AuthorZachary Neal Department of Sociology Michigan State University zpneal@msu.edu