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

Authors:
L. Egghe;R. Rousseau
Affiliations:
LUC, Universitaire Campus, B-3590 Diepenbeek, Belgium and UIA, IBW, Universiteitsplein 1, B-2610 Wilrijk, Belgium;KHBO, Industrial Sciences and Technology Zeedijk 101, B-8400 Oostende, Belgium and UIA, IBW Universiteitsplein 1, B-2610 Wilrijk, Belgium and LUC, Universitaire Campus, B-3590 Diepenbeek, Belgium
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2003

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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.