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the difference between an exponential and a scale-free network by visualizing a
network of 130 nodes and 215 links with the Paject program (Albert et al. 2000 ).
An exponential network is homogeneous in terms of the way links are distributed
between nodes. Most nodes have about the same number of links. A scale-free
network, on the other hand, is inhomogeneous, which means a few nodes have the
number of links much more than their “fair share” and the remaining nodes can
have as few as one or two links. It is these link-rich nodes that keep the entire
network stay in one piece. Pajek's network analysis functions allow the researchers
to visually demonstrate the crucial difference. The five “richest” nodes are colored
in red and their first neighbors are in green. In the exponential network, the five
most connected nodes reach only 27 % of the nodes. In contrast, in the scale-free
network, more than 60 % are reached.
The topology of a scale-free network provides an interesting point of reference
for us. Many visualizations of intellectual networks in subsequent chapters of this
topic are indeed very much resemble to the topology of a scale-free network,
although in many cases we achieve this by extracting a scale-free network from
a much larger network, which could be exponential.
If every vertex from a subset of all vertices is connected to at least k vertices
from the same subset, this subset of vertices is called k - core . If every vertex from a
subset is connected to every other vertex from the subset, such subsets of vertices
are called cliques .
Gephi is probably the most popular network visualization software currently
available. Building on the rich resources of the graph drawing and information
visualization communities, Gephi offers an extensible and user-friendly platform
to analyze and visualize large-scale networks. It is flexible and it supports popular
network formats such as GraphML and Pajek's .net format. In some areas, Gephi
has become competitive even to the most mature and widely used software available
from the earlier generations such as Pajek. It can gracefully handle large networks.
Figure 3.43 is an example generated based on a layout produced by Gephi and
rendered by CiteSpace. It shows an extensive network of 18,811 references shaped
by the citation behavior of 4,000 publications each year from 2000 till 2011 in
relation to regenerative medicine. The colors indicate the time of publication. Early
publications are in darker colors, whereas more recent ones are in yellow and orange
colors. Labels on the map highlight the names of authors of the most highly cited
references. The area that corresponds to the iPSCs cluster is located at the upper left
corner of the network in orange, where the names of Takahashi and Yu are labeled.
Networks visualized at this level may provide a good starting point to make sense of
the dynamics of the evolving field. On the other hands, the devils are in the details.
Differentiating topics, hypotheses, and findings at document is essential to the study
of an evolving scientific field.
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