Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Assessing Percolation Threshold Based on High-Order Non-Backtracking
  Matrices   Percolation threshold of a network is the critical value such that when nodes
or edges are randomly selected with probability below the value, the network is
fragmented but when the probability is above the value, a giant component
connecting large portion of the network would emerge. Assessing the percolation
threshold of networks has wide applications in network reliability, information
spread, epidemic control, etc. The theoretical approach so far to assess the
percolation threshold is mainly based on spectral radius of adjacency matrix or
non-backtracking matrix, which is limited to dense graphs or locally treelike
graphs, and is less effective for sparse networks with non-negligible amount of
triangles and loops. In this paper, we study high-order non-backtracking
matrices and their application to assessing percolation threshold. We first
define high-order non-backtracking matrices and study the properties of their
spectral radii. Then we focus on 2nd-order non-backtracking matrix and
demonstrate analytically that the reciprocal of its spectral radius gives a
tighter lower bound than those of adjacency and standard non-backtracking
matrices. We further build a smaller size matrix with the same largest
eigenvalue as the 2nd-order non-backtracking matrix to improve computation
efficiency. Finally, we use both synthetic networks and 42 real networks to
illustrate that the use of 2nd-order non-backtracking matrix does give better
lower bound for assessing percolation threshold than adjacency and standard
non-backtracking matrices.

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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph