Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Coding and Topological Matrices Toward Network Overall
  Security   A mathematical topology with matrix is a natural representation of a coding
relational structure that is found in many fields of the world. Matrices are
very important in computation of real applications, s ce matrices are easy
saved in computer and run quickly, as well as matrices are convenient to deal
with communities of current networks, such as Laplacian matrices, adjacent
matrices in graph theory. Motivated from convenient, useful and powerful
matrices used in computation and investigation of today's networks, we have
introduced Topcode-matrices, which are matrices of order $3\times q$ and differ
from popular matrices applied in linear algebra and computer science.
Topcode-matrices can use numbers, letters, Chinese characters, sets, graphs,
algebraic groups \emph{etc.} as their elements. One important thing is that
Topcode-matrices of numbers can derive easily number strings, since number
strings are text-based passwords used in information security. Topcode-matrices
can be used to describe topological graphic passwords (Topsnut-gpws) used in
information security and graph connected properties for solving some problems
coming in the investigation of Graph Networks and Graph Neural Networks
proposed by GoogleBrain and DeepMind. Our topics, in this article, are:
Topsnut-matrices, Topcode-matrices, Hanzi-matrices, adjacency ve-value matrices
and pan-Topcode-matrices, and some connections between these Topcode-matrices
will be proven. We will discuss algebraic groups obtained from the above
matrices, graph groups, graph networking groups and number string groups for
encrypting different communities of dynamic networks. The operations and
results on our matrices help us to set up our overall security mechanism to
protect networks.

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The categories of this paper are: stat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an