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

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. (C) 2003 Elsevier Science Ltd. All rights reserved.