Two Paradigms for Creating a Partition or a Partial Partition on a Graph

This chapter discusses the relative merits of partitions versus dead leaves models. In a watershed partition, each node is assigned to the catchment basin of one and only one black hole. Catchment basins do not overlap and form a partition of the domain. In a dead leaves model, the labels are assigned priorities and the catchment zones are stacked on top of one another, the most prioritary ones covering the less prioritary ones. The core‐expanding algorithm constructs a partition of the nodes in catchment basins, i.e. catchment zones with minimum overlapping. It uses the node weights and the arrows of the digraph. The chapter illustrates the pruning effect on the downstream of a node and the catchment zones containing it with two examples. Pruning the digraph is the source of great flexibility: upstream or downstream propagation of labels may be done locally, in any order.