Mapping Associations - Mapping Scientific Frontiers: The Quest for Knowledge Visualization - page 136

Mark Steyvers and Josh Tenenbaum analyzed three types of semantic networks:
associative networks, WordNet, and Roget's thesaurus (Steyvers and Tenenbaum
2001 ). They found that these semantic networks demonstrate some typical features
of a small-world structure: sparse, short average path-lengths between words, and
strong local clustering. In these semantic networks it was also found that the
distributions of the number of connections follow power laws, suggesting a hub
structure similar to the WWW. They built a network model that acquires new
concepts over time and integrates them into the existing network. If new concepts
grow from well-connected concepts and their neighbors in the network, this network
model demonstrates the small-world characteristics of semantic networks and the
power-law distributions in the number of connections. An interesting prediction
of their model is that concepts that are learned early in the network acquire more
connections over time than concepts learned late.
For an example of a shortest pathway running through major scientific disciplines
instead of concepts, see Henry Small's work on charting the pathways in scientific
literature (Small 2000 ), although he did not study these pathways as a small-
world phenomenon. In Chap. 5 , we will introduce another trailblazing example
from Small's work on specialty narratives (Small 1986 ). The small-world model
of semantic networks predicts that the earlier a concept is learned in the network,
the more connections it will get. This doesn't sound surprising. Sociologist Robert
Merton's Matthew's Effect, or the rich get richer, leads us to think the characteristics
of scientific networks. After all, the small-world phenomenon was originated from
the society. Practical implications of these small-world studies perhaps lie in how
one can find strong local clusters and build shortest paths to connect to these clusters.
These findings may also influence the way we see citation networks.

3.5.5 Network Visualization

3.5.5.1 Pajek

In Slovene, the word pajek means spider. A computer program Pa jek is designed
for analysis of large networks of several thousands of vertices (Batagelj and Mrvar
1998 ). It is freely available for noncommercial use. 4 Conventionally, a network with
more than hundreds of vertices can be regarded as large. There are even larger
networks, such as the Web, with estimated billions of web pages, forms a super-
large network.
Reka Albert, Hawoong Jeong, Albert-Laszlo Barabasi analyzed the error and
attach tolerance of complex networks. The tool they used was Pajek. They illustrated

4 http://vlado.fmf.uni-lj.si/pub/networks/pajek/