Ricky Ho explains these two fundamental graph papers
The execution model is based on BSP (Bulk Synchronous Processing) model. In this model, there are multiple processing units proceeding in parallel in a sequence of “supersteps”. Within each “superstep”, each processing units first receive all messages delivered to them from the preceding “superstep”, and then manipulate their local data and may queue up the message that it intends to send to other processing units. This happens asynchronously and simultaneously among all processing units. The queued up message will be delivered to the destined processing units but won’t be seen until the next “superstep”. When all the processing unit finishes the message delivery (hence the synchronization point), the next superstep can be started, and the cycle repeats until the termination condition has been reached.
Note that Google’s Pregel is at the very high level quite similar to Google’s MapReduce.