The Structure and Dynamics of Scientific Knowledge - Mapping Scientific Frontiers: The Quest for Knowledge Visualization - page 185

Fig. 5.16 A minimum
spanning tree solution of the
author co-citation network
based on the ACM Hypertext
dataset (Nodes D 367,
Links D 366)

connected symmetric matrix of this size would have a maximum of 66,978 links,
excluding self-citations. In other words, the co-citation patterns were about 91 %
of the maximum possible connectivity. The MST solution selected a total of 366
strongest links. It produces a much-simplified picture of the patterns.
MST provides explicit links to display a more detailed picture of the underlying
network. If the network contains equally weighted edges, one can arbitrarily choose
any one of the MSTs. However, an arbitrarily chosen MST destroys the semantic
integrity of the original network because the selection of an MST is not based on
semantic judgments. Pathfinder network scaling resolves this problem by preserving
the semantic integrity of the original network. When geodesic distances are used, a
Pathfinder network is the set union of all possible MSTs. Pathfinder selects links by
ensuring that selected links do not violate the triangle inequality condition.
Figure 5.17 is a Pathfinder network solution of the same author co-citation
matrix. Red circles mark the extra links when comparing to an MST solution. A total
of 398 links were included in the network - the pathfinder network was 32 links
more than the number of links in its MST counterpart solution. These extra links
would be denied in MST because they form cyclic paths, but forming a cyclic path
alone as a link selection criterion may overlook potentially important links.
In order to incorporate multiple aspects of author co-citation networks, we
emphasize the significance of the following aspects of ACA (See Fig. 5.18 ):

• Represent an author co-citation network as a Pathfinder network;

• Determine specialty memberships directly from the co-citation matrix using

PCA;

• Depict citation counts as segmented bars, corresponding to citation counts over

several consecutive years.