Article
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A Set-theoretic Approach to Modeling Network Structure
Version 1
: Received: 27 March 2021 / Approved: 30 March 2021 / Online: 30 March 2021 (09:31:31 CEST)
A peer-reviewed article of this Preprint also exists.
Pfaltz, J.L. A Set-Theoretic Approach to Modeling Network Structure. Algorithms 2021, 14, 153. Pfaltz, J.L. A Set-Theoretic Approach to Modeling Network Structure. Algorithms 2021, 14, 153.
Abstract
Three computer algorithms are presented. One reduces a network $\CALN$ to its interior, $\CALI$. Another counts all the triangles in the network, and the last randomly generates networks similar to $\CALN$ given just its interior $\CALI$. But these algorithms are not the usual numeric programs that manipulate a matrix representation of the network; they are set-based. Union and meet are essential binary operators; contained_in is the basic relational comparator. The interior $\CALI$ is shown to have desirable formal properties and to provide an effective way of revealing ``communities'' in social networks.
Keywords
closure; interior; network generation; community; eigenvector
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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