CONNECTIONS - INSNA

CONNECTIONS
Multiplicity and Redundancy
The last section of Table 5 summarizes the
precise configurations of ties. Recall in our
discussion of Figure 4, there were potentially
eight types of ties. However, when aggregated,
only seven distinct patterns of social affiliations
are represented– corporate only, university only
and social club only (note there were no ties that
were only based on shared affiliations through
museums since all of those ties were structurally
redundant). Table 5 shows that only a quarter of
the ties were from corporate ties alone. While
fewer than 3 percent of the ties were formed
solely through shared university ties, over a
quarter (26.28 percent) of the ties were based
exclusively on mutual social club memberships.
The bottom section of Table 5 also shows that
over a third of the ties between these 20
directors were constituted by both corporate and
social club ties. Equally important from the
perspective of emphasizing the role of noncorporate
ties in integrating our corporate
directors, 7 ties were based on two or more
noncorporate ties. Finally, Table 5 indicates that
6 of the 137 ties were from three or more
sources, including at least one corporate tie. In
short, the results in Table 5 underscore the
message from Figure 4 – non-corporate ties
constitute a substantial portion of the social
connections between our example directors, with
social club ties being most abundant.
Thus far, the discussion has focused on how to
represent the multiplicity of ties between the
directors in this example network. However, it
would also be useful to further aggregate these
various configurations of ties back to the
individual directors. To accomplish this
aggregation, the analyses revert to the original
set of 207 ties. However, rather than
aggregating on the basis of the tie ID itself (1.02,
1.16 or 1.08), this time we need to aggregate by
the vertex number (making sure that both
sending and receiving vertices are represented).
Therefore, by shifting the level of analysis back
to the directors themselves, each director will
possess a set of ties that can be characterized by
being completely or predominantly corporate.
In contrast, a director’s set of ties can be
primarily grounded in other organizational
affiliations. Consider again John A. Barr. This
time however, Table 6 presents all of his 33 ties
with the 19 other directors.
By sorting the ties by type, it is straightforward
to calculate both the sum of strengths which
reflects the 33 individual ties, and the sum of the
strengths for each type of tie. 3 Table 6 shows
that of the 33 ties, 9 are based on shared
corporate board memberships, 2 on mutual
membership on university Boards of Regents or
Trustees, and 22 on shared social club
memberships. This means that 27.3 percent of
John Barr’s ties were corporate, 6 percent were
university and 66.7 percent were social club
based. When this procedure is applied to the
remaining 19 directors, we can then obtain
summary measures of the configuration of ties
possessed by each director. Table 7 presents the
summary statistics for the 20 directors in this
example.
Table 7. Configuration of Ties for Directors
Average Proportion of Corporate Ties 0.4990
Average Proportion of Museum Ties 0.0215
Average Proportion of University Ties 0.0540
Average Proportion of Social Club Ties 0.4255
Therefore, on average, the twenty directors are
characterized by half of their ties being
corporate based, and nearly another half are
based on social club ties. Finally, Table 7
indicates that the average percent of ties based
on museum ties is only 2.15 percent and the
average percent of ties based on shared
university ties is 5.4 percent. In other words,
this example of 20 directors is tied together by
both corporate and club ties in roughly equal
proportions. While this conclusion is far from
3 Calculating the degree of each director on the basis
of each of the four affiliation matrices would yield
the number of different directors tied to John Barr
and as a consequence, we would lose the multiple
corporate ties between this director and David
Kennedy, and the multiple club ties between John
Barr and G.A. Freeman Jr., Paul W. Goodrich, R.S.
Ingersoll, David Kennedy, H.J. Livingston, Brooks
McCormick, James F. Oats Jr., and J. Harris Ward.
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