  We study the problem of erasure correction (node repair) for regenerating
codes defined on graphs wherein the cost of transmitting the information to the
failed node depends on the graphical distance from this node to the helper
vertices of the graph. The information passed to the failed node from the
helpers traverses several vertices of the graph, and savings in communication
complexity can be attained if the intermediate vertices process the information
rather than simply relaying it toward the failed node. We derive simple
information-theoretic bounds on the amount of information communicated between
the nodes in the course of the repair. Next we show that Minimum Storage
Regenerating (MSR) codes can be modified to perform the intermediate
processing, thereby attaining the lower bound on the information exchange on
the graph. We also consider node repair when the underlying graph is random,
deriving conditions on the parameters that support recovery of the failed node
with communication complexity smaller than required by the simple relaying.
