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Reliability of rank order in sampled networks
In complex scale-free networks, ranking the individual nodes based upon their
importance has useful applications, such as the identification of hubs for
epidemic control, or bottlenecks for controlling traffic congestion. However,
in most real situations, only limited sub-structures of entire networks are
available, and therefore the reliability of the order relationships in sampled
networks requires investigation. With a set of randomly sampled nodes from the
underlying original networks, we rank individual nodes by three centrality
measures: degree, betweenness, and closeness. The higher-ranking nodes from the
sampled networks provide a relatively better characterisation of their ranks in
the original networks than the lower-ranking nodes. A closeness-based order
relationship is more reliable than any other quantity, due to the global nature
of the closeness measure. In addition, we show that if access to hubs is
limited during the sampling process, an increase in the sampling fraction can
in fact decrease the sampling accuracy. Finally, an estimation method for
assessing sampling accuracy is suggested
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