Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# 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)

How to cite: Pfaltz, J. A Set-theoretic Approach to Modeling Network Structure. Preprints 2021, 2021030715 (doi: 10.20944/preprints202103.0715.v1). Pfaltz, J. A Set-theoretic Approach to Modeling Network Structure. Preprints 2021, 2021030715 (doi: 10.20944/preprints202103.0715.v1).

## 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.

## Subject Areas

closure; interior; network generation; community; eigenvector

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