Fig. 1. Random walks with metadata-dependent encoding probabilities.

In this schematic example with single, long random walks, we encode the random walks’ next step if the target node’s metadata are the same as for the previously encoded node. When the metadata differ, encoding with a probability between 33 and 100% gives the solution in (A), between 10 and 33% gives the solution in (B), and less than 10% gives the solution in (C). Node shapes represent metadata, and node colors represent optimal partitions. The random walks are colored by the currently encoded module and labeled with circles when they encode a transition and with dotted lines when they skip nodes. The alphabetic codes represent the walks with this metadata-dependent encoding scheme.