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help for centpow
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Network Centrality and Power

        centpow filename , [ normalize beta(real) saveas(filename)]


Description

    centpow creates 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 by filename.
    [NOTE: This command does not affect the data in memory.]


Options
    normalize Requests that each measure be normalized using the approach
        described by Bonacich (1987).
    beta(real) Specifies the value of the beta parameter 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 is centpow.dta.


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


Output
    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.

    Degree 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 variable alterpow.

    Beta centrality and power are saved as the variables betacent and
    betapow, 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 beta is 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.
 


References

Neal, Z. P. (2011) Differentiating Centrality and Power in the World City
     Network, Urban Studies 48: 2733-2748. (CLICK FOR PDF)

Neal, J. W. and Z. P. Neal.  (in press) Power as a Structural Phenomenon,
     American Journal of Community Psychology 48: 157-167. (CLICK FOR PDF)

Bonacich, P.  (1987) Power and Centrality: A Family of Measures, American
     Journal of Sociology 92: 1070-82.


Author

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