Conveying discrete memoryless sources over networks: When are zero-rate edges dispensable?

This work investigates the problem of conveying discrete memoryless sources over general networks with specified lossless (vanishing error probability) and/or lossy (average per-symbol distortion) reconstruction demands. It presents two different sufficient conditions under which an edge carrying zero-rate messages is not crucial for the conveyance of the sources, i.e., the demands can be met even when the zero-rate edge is deleted and the rates on other edges are kept unchanged.