Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic Centralization of Some Graph Families   Centrality describes the importance of nodes in a graph and is modeled by
various measures. Its global analogue, called centralization, is a general
formula for calculating a graph-level centrality score based on the node-level
centrality measure. The latter enables us to compare graphs based on the extent
to which the connections of a given network are concentrated on a single vertex
or group of vertices. One of the measures of centrality in social network
analysis is harmonic centrality. It sums the inverse of the geodesic distances
of each node to other nodes where it is 0 if there is no path from one node to
another, with the sum normalized by dividing it by $m-1$, where $m$ is the
number of nodes of the graph. In this paper, we present some results regarding
the harmonic centralization of some important families of graphs with the hope
that formulas generated herein will be of use when one determines the harmonic
centralization of more complex graphs.

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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys