  In this paper, a hub refers to a non-terminal vertex of degree at least
three. We study the minimum number of hubs needed in a network to guarantee
certain flow demand constraints imposed between multiple pairs of sources and
sinks. We prove that under the constraints, regardless of the size or the
topology of the network, such minimum number is always upper bounded and we
derive tight upper bounds for some special parameters. In particular, for two
pairs of sources and sinks, we present a novel path-searching algorithm, the
analysis of which is instrumental for the derivations of the tight upper
bounds.
