24 Graphs and DFS

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A path in a graph is a sequence of nodes such that adjacent nodes are joined by an edge. A path has the obvious meaning if you think of the graph as a highway map. In the example above, there is no edge from A to D, but there is a path going through C. We would write that path as ACD. Similarly, there is a path from B to D, which is BCD. But there is no path ABD, because the edge from B to D is missing. A cycle in a graph is a path with the same start and end node. In the example above, there is a cycle ABCA. A graph is said to be
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online