Figure 1. An adjustable hierarchical network with the different edge types.

The blue edges belong to the original arborescence graph that is used as the backbone of the adjustable hierarchical (AH) network. There are three type of possible edges added to the graph: down edges (green), horizontal edges (orange) and up edges (red). They have different effects on the hierarchical structure of the directed tree. Down edges conserve the hierarchy, horizontal edges has a slight influence and up edges make strong changes in the structure.