CONNECTIONS - INSNA

CONNECTIONS
Multiplicity and Redundancy
Beginning with the set of visualizations in
Figure 3, the analyses use the network of
corporate ties as a point of departure. Note that
the widths of the arcs vary to represent the
strength of the particular tie and the colors of the
vertices are coded to represent their highest level
of multiplicity. For example, in the network of
corporate ties alone, we see two pairs of
directors that are red indicating that each has at
least one tie that is of strength 3 – meaning that
there are three corporate ties linking these two
directors. Further, the tie between the two red
vertices is clearly thicker than the other edges in
the network which have strengths of 1 or 2.
Finally, all of the other vertices in the network
are green indicating that they have at least one
tie with a strength value of 2.
In the subsequent networks in Figure 3, ties from
each set of noncorporate organization are
superimposed on the network of corporate ties.
This is accomplished by treating corporate ties
as arcs in one direction while the ties from say
museums are graphed as arcs in the opposite
direction. Looking at the network of corporate
ties with museum ties added, we see first, that
there are relatively few ties added. Furthermore,
if we examine the yellow orange ties that are
added from shared affiliations with museums,
the majority of the arcs are bi-directed indicating
that they simply reinforce an existing corporate
tie. In contrast, note the third graph in which the
red ties in the lower right corner of the graph are
clearly new ties formed through university board
affiliations (although the tie between Rockefeller
and Livingston is slightly obscured by other
corporate ties). Finally, the fourth graph with
cyan ties dramatically underscores the number
of ties between these 20 directors that are
formed through shared club memberships.
While the different configuration of each
individual set of ties is certainly noteworthy, the
sociographs in Figure 3 do not allow us to
display the simultaneous set of ties from all
organizations. To pull all of this information
together and to capture multiple types of ties
between a given pair of directors, it is necessary
to aggregate the ties so as to preserve the types
and strengths of all of the ties. To accomplish
this condensing/preservation of information, we
have assigned two values to each tie between
directors – a strength code and a type code.
Consider the following sample of seven ties
between John Barr and three other directors
(Table 4).
Table 4. Individual Ties with John A. Barr (01)
Tie ID Director (vertex #) Strength Type Code Type of Tie
1.02 Block, Joseph L. (02) 1 100000 Corporation
1.02 Block, Joseph L. (02) 1 1 Club
2 100001 Aggregated Sum
1.16 Oates, James F. Jr. (16) 1 100 University
1.16 Oates, James F. Jr. (16) 2 1 Club
3 101 Aggregated Sum
1.08 Gale, Willis (08) 1 100000 Corporation
1.08 Gale, Willis (08) 1 100 University
1.08 Gale, Willis (08) 1 1 Club
3 100101 Aggregated Sum
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