Chapter9 graph data structure
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This document discusses graphs and their representation in code. It defines graphs as consisting of vertices and edges, with edges specified as pairs of vertices. It distinguishes between directed and undirected graphs. Key graph terms like paths, cycles, and connectivity are defined. Real-world systems that can be modeled as graphs are given as an example. The document then discusses representing vertices and edges in code, choosing an adjacency matrix to represent the edges in the graph.
Chapter9 graph data structure
- 1. DATA STRUCTURE Chapter 9: Graph Prepared & Presented by Mr. Mahmoud R. Alfarra 2011-2012 College of Science & Technology Dep. Of Computer Science & IT BCs of Information Technology http://mfarra.cst.ps
- 2. Out Line What is a graph ? What is a directed graph? What is an Unordered graph? Graph’s terms Real world systems modeled by graphs The Graph class Representing Vertices Representing Edges Adjacency matrix 2
- 3. What is a graph ? A graph consists of a set of vertices and a set of edges. Think of a map of your state. A map is a type of graph. Each town is a vertex and a road that connects two towns is an edge. Edges are specified as a pair, (v1, v2), where v1 and v2 are two vertices in the graph. A vertex can also have a weight, sometimes also called a cost. 3
- 4. What is a directed graph? 4 A graph whose pairs are ordered is called a directed graph, or just a digraph.
- 5. What is an Unordered graph? 5 If a graph is not ordered, it is called an unordered graph, or just a graph.
- 6. Graph’s terms 6 A path is a sequence of vertices in a graph such that all vertices are connected by edges. The length of a path is the number of edges from the first vertex in the path to the last vertex. A path can also consist of a vertex to itself, which is called a loop. Loops have a length of 0. A cycle is a path of at least 1 in a directed graph so that the beginning vertex is also the ending vertex. In a directed graph, the edges can be the same edge, but in an undirected graph, the edges must be distinct.
- 7. Connected Graph 7 البيانات تراكيب مساق إعداد العلمية المادة / أ . ا َّالفــر رفيق محمود An undirected graph is considered connected if there is a path from every vertex to every other vertex.
- 8. Connected Graph 8 In a directed graph, this condition is called strongly connected. A directed graph that is not strongly connected, but is considered connected, is called weakly connected. If a graph has an edge between every set of vertices, it is said to be a complete graph.
- 9. Real world systems modeled by graphs 9 Graphs are used to model many different types of real world systems. One example is traffic flow. The vertices represent street intersections and the edges represent the streets themselves. Weighted edges can be used to represent speed limits or the number of lanes.
- 10. The Graph class 10 At first glance, a graph looks much like a tree and you might be tempted to try to build a graph class like a tree. There are problems with using a reference based implementation, however, so we will look at a different scheme for representing both vertices and edges. Vertices Edges Graph
- 11. Representing Vertices 11 The first step we have to take to build a Graph class is to build a Vertex class to store the vertices of a graph. This class has the same duties the Node class had in the LinkedList and BinarySearchTree classes. The Vertex class needs two data members: 1. One for the data that identifies the vertex. 2. The other a Boolean member we use to keep track of “visits” to the vertex.
- 12. Representing Edges 12 We will store the list of vertices in an array and will reference them in the Graph class by their position in the array. The method we’ll choose for representing the edges of a graph is called an adjacency matrix. This is a two-dimensional array where the elements indicate whether an edge exists between two vertices.
- 13. Adjacency matrix 13 The vertices are listed as the headings for the rows and columns. If an edge exists between two vertices, a 1 is placed in that position. If an edge doesn’t exist, a 0 is used. Obviously, you can also use Boolean values here.
- 14. Thank You … 14 Remember that: question is the key of knowledge
- 15. Ahl Eljanna ْلا ا َلِإ ا تْ وا ْملا اا يهِف ا نوُقوُ ذاي ا َل اقا وا و ا وَلُْ اْل اةاتْ وا م ا ابا ذا ع ْ مُ اه ِ يمِ حاْ ْلا 15