111. These figures schematically show the process of creating an overlay spanning tree on an unweighted graph which may represent the road map of a city.
222. These figures schematically show the process of how a graph can be divided into hierarchical clusters of neighboring nodes which are not further than a specific value from each other.
333. These figures show the benefit of multi-level (hierarchical) partitioning in a graph which will lead to an expandable routing scheme for a graph of any size.
444. These figures show the process of decomposing a graph into different clusters with smaller diameters.
555. These figures show the hierarchical nature of graph decomposition and how it helps to create an expandable routing scheme for a graph of any size.
666. Outline of graph decomposition for the first three levels.