On the Impact of a Single Edge on the Network Coding Capacity

In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes. More precisely, we study the change in network capacity that results when we remove a single link of capacity $\delta$. In a recent result, we proved that if all the sources are directly available to a single super-source node, then removing a link of capacity $\delta$ cannot change the capacity region of the network by more than $\delta$ in each dimension. In this paper, we extend this result to the case of multi-source, multi-sink networks for some special network topologies.