Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Walks: A Beginner's Guide to Graphs and Matrices
Yuki IRIE
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JOURNALS FREE ACCESS Advance online publication

Article ID: 2020.A.01

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Abstract

We provide an introduction to graph theory and linear algebra. The present article consists of two parts. In the first part, we review the transfer-matrix method. It is known that many enumeration problems can be reduced to counting walks in a graph. After recalling the basics of linear algebra, we count walks in a graph by using eigenvalues. In the second part, we introduce PageRank by using a random walk model. PageRank is a method to estimate the importance of web pages and is one of the most successful algorithms. This article is based on the author's lectures at Tohoku University in 2018 and 2020.

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© 2020 by the Graduate School of Information Sciences (GSIS), Tohoku University
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