Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PageRank for evolving link structures   In this article we will look at the PageRank algorithm used as part of the
ranking process of different Internet pages in search engines by for example
Google. This article has its main focus in the understanding of the behavior of
PageRank as the system dynamically changes either by contracting or expanding
such as when adding or subtracting nodes or links or groups of nodes or links.
In particular we will take a look at link structures consisting of a line of
nodes or a complete graph where every node links to all others.
  We will look at PageRank as the solution of a linear system of equations and
do our examination in both the ordinary normalized version of PageRank as well
as the non-normalized version found by solving the linear system. We will see
that it is possible to find explicit formulas for the PageRank in some simple
link structures and using these formulas take a more in-depth look at the
behavior of the ranking as the system changes.

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The categories of this paper are: physics
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph