  We consider network models where information items flow %are sent from a
source to a sink node. We start with a model where routing is constrained by
energy available on nodes in finite supply (like in Smartdust) and efficiency
is related to energy consumption. We characterize graph topologies ensuring
that every saturating flow under every energy-to-node assignment is maximum and
provide a polynomial-time algorithm for checking this property. We then
consider the standard flow networks with capacity on edges, where again
efficiency is related to maximality of saturating flows, and a traffic model
for selfish routing, where efficiency is related to latency at a Wardrop
equilibrium. Finally, we show that all these forms of inefficiency yield
different classes of graphs (apart from the acyclic case, where the last two
forms generate the same class). Interestingly, in all cases inefficient graphs
can be made efficient by removing edges; this resembles a well-known
phenomenon, called Braess's paradox.
