24 Graphs and DFS

# 24 Graphs and DFS - Chapter 24 Graphs and DFS Motivation...

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Chapter 24: Graphs and DFS Motivation Graphs are among the most general and important data structures. They are used to represent a set of objects and a relation among the objects. In engineering problems, they are used to represent electrical circuits, chemical molecules, highway maps, manufacturing processes, and structural and geometric models. In this chapter we will introduce graphs, give a few of their properties, and define an important algorithm on graphs called depth-first search or DFS. Graphs A graph consists of nodes (or vertices ) and edges . Each node holds some data, and an edge joins two nodes. In the example below, the nodes are A, B, C, D. The edges are written as the set of nodes that they join. So the edge from A to C is written {A, C}. The list of all the edges is the graph is [{A, B} {A, C} {B, C} {C, D}]. The graph above is an undirected graph. That means that we can write {A, B} or {B, A} and we mean the same edge. In a directed graph, we would write (A, B) for an edge from A to B, and (B, A) for an edge from B to A. These would be different edges. We indicate the direction with an arrowhead. So in a directed graph, an edge from A to B would be written: Paths in Graphs

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