Graphics Reference
In-Depth Information
significant resources and capital were controlled by 341 directors held
across 112 corporations by members of a small group of financial
institutions, with J.P. Morgan figuring in prominently. These findings led to
new extensions to antitrust laws.
These organizational and genealogical charts depict hierarchies that are
a special kind of graph that can be useful when analyzing and depicting
graphs.
Trees and Graphs
In graph terminology, a hierarchy can be called a
tree
. In a tree, no paths
are cycles (circular paths), and there exists only one path between any two
nodes. The number of links in an
undirected tree
is always equal to the
number of nodes less one. Beyond the idea of a social hierarchy, many
different data sets are trees or, more importantly, can be analyzed as trees.
The trees shown in
Figure 10-2
and
Figure 10-3
are extracted from larger
graphs. For example, the genealogy chart (
Figure 10-2
) has references to
other family trees as royalty married across families from different
countries. Or, in the case of the Pujo Committee Report (
Figure 10-3
)
,
directors of large companies may have had connections across companies
without being connected to J.P. Morgan.
Any graph can be turned into a tree to answer simple questions about
the graph. A
spanning tree
is a graph where some of the edges have
been discarded so that no cycles remain—leaving a tree.
Figure 10-4
shows
a graph and a corresponding spanning tree. Note that many different
spanning trees can be created from the same graph, so the edges that are
kept should correspond to the objective.
