Information Technology Reference
In-Depth Information
Just as in geographic mapping, the cartographer makes decisions about scale and
detail depending on the intended uses of the map. There is no hard and fast rule to
determine the best number of clusters can be selected.
In Trochim's concept mapping, rating data was used to provide the third-
dimension on a 2-dimensional map, a vertical overlay that depicts the height of
various regions. In a cluster map, the layers of a cluster depicted the average
importance rating of all statements within the cluster.
Meaningful text labels are essential to identify the nature of point groupings
and clusters simple and clear. Automatically generating meaningful labels is still
a challenge. The most straightforward way to generate labels is to ask people to
do it. If individuals gave different labels, simply choose the label that makes most
sense.
3.5
Network Models
Graph theory is a branch of mathematics that studies graphs and networks. A graph
consists of vertices and edges. A network consists of nodes and links. Many impor-
tant phenomena can be formulated as a graph problem, such as telecommunication
networks, club membership networks, integrated electric circuits, and scientific
networks. Social networks, for example, are graphs in which vertices represent
people and edges represent interrelationships between people. Acquaintanceship
graphs, co-author graphs, and collaboration graphs are examples of social networks.
To a mathematician, they are essentially the same thing. In graph theory, the focus
is on the connectivity of a graph - the topology, rather than the geometry. One of
the earliest graph theoretical studies was dated back to 1736 when Leonhard Euler
(1707-1783) published his paper on the solution of the Konigsberg bridge problem.
Another classical problem in graph theory is the famous Traveling Salesman
Problem (TSP). In the twentieth-century graph theory has become more statistical
and algorithmic, partly because we are now dealing with some very large graphs
such as the Web, telephone call graphs, and collaboration graphs. In this section,
two types of graphs are of particular interest to us: random graphs and small-world
networks.
3.5.1
Small-World Networks
The phrase “ six degrees of separation ” describes the phenomenon of a small
world where any random two people can discover a link through a chain of six
acquaintances. Ithiel de Sola Pool (1917-1984) pioneered the study of contact
networks, a line of work that becomes known as “the small world” phenomenon
(Kochen 1989 ). There was even a movie called “Six Degrees of Separation.”
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