Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cospectral family of graphs for the normalized Laplacian found by
  toggling   We give a construction of a family of (weighted) graphs that are pairwise
cospectral with respect to the normalized Laplacian matrix, or equivalently
probability transition matrix. This construction can be used to form pairs of
cospectral graphs with differing number of edges, including situations where
one graph is a subgraph of the other. The method used to demonstrate
cospectrality is by showing the characteristic polynomials are equal.

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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio