BRS-compactness in networks: Theoretical considerations related to cohesion in citation graphs, collaboration networks and the internet

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Abstract

Compactness as introduced by Botafogo, Rivlin and Shneiderman, in short: BRS-compactness, is studied in general, as it can be used to describe the cohesion of parts of the internet or collaboration networks, and in the particular case of a unidirectional network, such as a citation graph. It is shown that the connection coefficient is an upper bound for the BRS-compactness value of a network. During our investigations, we derive an upper bound for the generalized Wiener index of a directed graph. Several networks are constructed and their BRS-compactness values are calculated.

Keywords

BRS-compactness
Networks
Hyperlinks
Internet
Citation networks
Collaboration graphs
Generalized Wiener index
Sum of distances in a graph

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