Graph Theory: A Primer for Using R Visualization Techniques in the Applications of the Adjacency Matrix
21 Pages Posted: 21 Oct 2010 Last revised: 22 Dec 2010
Date Written: October 19, 2010
Today, graph theory has become major instrument that is used in an array of fields. Some of these include electrical engineering, mathematical research, sociology, economics, computer programming/networking, business administration and marketing. Indeed, many problems can be modeled with paths formed by traveling along the edges of a certain graph. Frequently referenced problems are efficiently planning routes for mail delivery, garbage pickup and snow removal, which can be solved using models that involve paths in graphs. Given these kinds of problems, graphs can become extremely complex, and a more efficient way of representing them is needed in practice. This is where the concept of the adjacency matrix and linear algebra comes into play. This paper develops the linear algebra application to the adjacency matrix and then presents some visuals in the form of sample graphs and attributes, as well as an interactive version.
This paper is a part of a sequence of papers that responds to different aspects of graph theory. Please refer to the author’s research page at http://ssrn.com/author=1555152
Keywords: Graphy Theory, Max Plus Algebra, R
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