CONNECTIONS - INSNA

CONNECTIONS
Multiplicity and Redundancy
extra-corporate relation, the issue of capturing
the multiplicity of ties does not arise in these
studies.
One of the classic problems accompanying the
examination of affiliation network data is the
loss of information when relations and ties are
reduced from two-modes to a single mode
(Field, Frank, Schiller, Riegle-Crumb & Mulle,
2006). When networks are reduced to a single
mode, the duality of social experience – the
intersection of actors and events described by
Breiger (1974) – is no longer fully captured. As
noted by Bonacich and Domhoff (1981), there
are few methods that preserve the duality of
persons and groups. Instead, researchers must
rely on techniques that focus on a single set of
actors or events, such as the directors of large
American corporations in the present study. The
methods that do exist to preserve information
from both modes have focused chiefly on
identifying sets of actors, clusters, and structural
positions, rather than the contributions and
configurations of types of ties across social
space (See Laumann & Knoke 1987, Skvoretz &
Faust 1999 and Doreian et al 2004 for examples
of techniques.)
A second problem with affiliation data (as with
all valued networks) is the loss of information
that occurs when valued ties are dichotomized in
order to facilitate analysis. As noted by Thomas
and Blitzstein (2009), the transformation of
valued data to binary data creates analytical
uncertainty and may result in the loss of
significant information. In the case of an
affiliation matrix of corporate directors, the
value of each tie represents the number of joint
corporate, museum, university and social club
affiliations shared by a set of directors. When
ties are simply dichotomized, the relative value
or the importance of any given type of relation is
obscured. Opsahl, Agneessens and Skvoretz
(2010) have recently introduced a refined set of
algorithms to measure mode centrality in
weighted (valued) networks. While certainly a
step forward, these techniques still do not
preserve the information captured by the
multiplicity of ties. That is, they still do not
capture which relations are the most important to
the actors and the network.
In this paper, we describe a method of
preserving important information about the
context and configuration of ties while still
allowing for ease of analysis with standard
algorithms such as measures of centrality and
density. Our method is unique in that it allows
us to understand the context in which ties are
formed and to judge the types of relational ties
that are most important or valuable. Central to
this project of answering Burris’ call for a richer
sociology of elites are the concepts of structural
redundancy and the multiplicity of ties.
Structural Redundancy and the Multiplicity
of Ties
Redundancy
Structural redundancy is best thought of as the
opposite of a unique effect which occurs when
new ties emerge in a network of interlocking
corporate directors once the affiliations from
other non-corporate organizations are included.
On a more technical note, if additional ties are
detected following the addition of two (or more)
affiliation matrices and dichotomization of those
ties, then unique ties exist. Similarly, if there
are differences in the structure of the network
generated by the affiliations from two (or more)
organizations in comparison to the network of
corporate ties alone, then the ties added are not
redundant to the existing ties. In this paper, we
will use four simple measures of network
structure – network density, average degree,
average betweenness, and average geodesic
distance to highlight the unique contribution
made by additional ties, or highlighting which
ties are not redundant.
Methodologically, capturing the unique effects
of adding one set of ties is straightforward and
consists of simply comparing the network
density, average degree, average betweenness
and average geodesic distance of a network of
directors without and with the additional ties.
However, the methods are somewhat more
complicated if we want to consider the unique
effects of adding, say, the ties from university
board memberships while controlling for the
effects of all the other non-corporate ties. Here,
we would need to compare a different set of
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