Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-Isometric Graph Simplifications   We propose a general framework that uses quasi-isometries to study graph
simplifications. Quasi-isometries are mappings on metric spaces that preserve
the distance functions up to a multiplicative factor and an additive constant.
Quasi-isometries can be used to measure the distance distortion between the
original graph and the simplified graph.
  We then introduce a novel concept called the centre-shift, which quantifies
how much a graph simplification affects the location of the graph centre. Given
a quasi-isometry, we establish a weak upper bound on the centre-shift.
  We also present methods to construct so-called partition-graphs, which are
essentially graph minors with extra diameter bounds. We show that
partition-graphs are quasi-isometric to the original graph. Furthermore, in
terms of the centre-shift, we show that partition-graphs constructed in a
certain way preserve the centres of trees. Finally, we also show that
vertex-weighted partition-graphs preserve the median of trees.

5
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: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg