The Bonacich measure is a function of the entire structure.
Suppose in calculating centrality you weighted each connection to an
individual by that connection's degree. This produces a new set of
centrality scores, C1. Then instead of using degree you used C1 as
weights to calculate a new set of centrality scores, C2. C2 indirectly
includes the degrees of positions at a distance of 2 from the focal
actor. Then you continued this process (normalizing the scores at every
state so that don't get too big) until an equilibrium is reached. This
will be the eigenvector measure of centrality. Clearly, the whole
structure is involved.
Department of Sociology
University of California
Los Angeles, CA 90095
From: Social Network Researchers [mailto:[log in to unmask]] On Behalf
Of Andrew V. Shipilov
Sent: Tuesday, March 19, 2002 9:48 AM
To: [log in to unmask]
Subject: measures of power in social networks
I have a question about measuring power/status of an actor in a network.
What are the indices, other than Bonacich's power, that explicitly
incorporate centrality not only of a focal player, but also that of its
alters? Bonacich's measure uses degree centrality of a focal player and
adjusts it by the degree centrality of the players' alters, right? But
if this is the case, then that measure does not take into account the
overall structure of a network.
For the instances when a researcher is interested in studying status of
an actor as a function of its position in the overall network PLUS the
positions of its immediate alters in the overall network, would it not
make sense to use betweeness centrality to compute Bonacich's power
index? Has someone used similar measure already?
Thank you as always.
Andrew V. Shipilov
Strategic Management and Organization Theory
Joseph L. Rotman School of Management
University of Toronto
105 St. George Street
Toronto, ON, Canada