Hive as well as other Apps are going to have to ship configuration to the actual Processors.
The requested API would let you attach (static) data to each vertex and edge as well as the DAG itself at the time the DAG is assembled. The expectation is that the Processor has a structured way to retrieve that data for itself (the vertex) any edge connected to it as well as the overall "DAG" config.
The shape of the configuration could be anything. At a minimum having a byte buffer would be sufficient (up to the app what serialization to use for the config).