Weighted Graphs

This chapter introduces graphs, collections of nodes or vertices linked by undirected edges or directed arcs. It discusses two types of graphs: node‐weighted graphs and edge‐weighted graphs. Graphs are simple and abstract structures that are able to model all kinds of relations. Node‐weighted graphs may be used for modeling a topographic surface. Edge‐weighted graphs may be used for modeling the relations between the catchment zones of a topographic surface. Some nodes in a node‐weighted graph are surrounded by nodes with a higher weight. Such nodes are isolated regional minima nodes. In a node‐weighted graph, each edge is a flowing edge for its extremity holding the highest weight. The chapter analyzes and compares the "topography" of both edge‐weighted and node‐weighted graphs. The topography is described by analyzing the trajectories followed by a drop of water moving from node to node.