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DOI: 10.7155/jgaa.00505
Density decompositions of networks
Vol. 23, no. 4, pp. 625651, 2019. Regular paper.
Abstract We introduce a new topological descriptor of a graph called the
density decomposition which is a partition of the vertices of a graph
into regions of uniform density. The decomposition we define is
unique in the sense that a given graph has exactly one density
decomposition. The number of vertices in each partition defines a
density distribution which we find is measurably similar to the
degree distribution of given realworld networks (social, internet,
etc.) and measurably dissimilar in synthetic networks (preferential
attachment, small world, etc.).
We also show how to build networks having given density distributions, which gives us further insight into the structure of realworld networks.

Submitted: February 2018.
Reviewed: June 2019.
Revised: July 2019.
Accepted: July 2019.
Final: July 2019.
Published: September 2019.
Communicated by
Ulrik Brandes

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