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Locating Eigenvalues in Graphs - Algorithms and Applications (Paperback, 1st ed. 2022)
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Locating Eigenvalues in Graphs - Algorithms and Applications (Paperback, 1st ed. 2022)
Series: SpringerBriefs in Mathematics
Expected to ship within 10 - 15 working days
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This book focuses on linear time eigenvalue location algorithms for
graphs. This subject relates to spectral graph theory, a field that
combines tools and concepts of linear algebra and combinatorics,
with applications ranging from image processing and data analysis
to molecular descriptors and random walks. It has attracted a lot
of attention and has since emerged as an area on its own. Studies
in spectral graph theory seek to determine properties of a graph
through matrices associated with it. It turns out that eigenvalues
and eigenvectors have surprisingly many connections with the
structure of a graph. This book approaches this subject under the
perspective of eigenvalue location algorithms. These are algorithms
that, given a symmetric graph matrix M and a real interval I,
return the number of eigenvalues of M that lie in I. Since the
algorithms described here are typically very fast, they allow one
to quickly approximate the value of any eigenvalue, which is a
basic step in most applications of spectral graph theory. Moreover,
these algorithms are convenient theoretical tools for proving
bounds on eigenvalues and their multiplicities, which was quite
useful to solve longstanding open problems in the area. This book
brings these algorithms together, revealing how similar they are in
spirit, and presents some of their main applications. This work can
be of special interest to graduate students and researchers in
spectral graph theory, and to any mathematician who wishes to know
more about eigenvalues associated with graphs. It can also serve as
a compact textbook for short courses on the topic.
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