1. Graphs

2. Graphs
Graphs is a data structure that differ from all the others in one major concept , each node may have multiple predecessors as well as multiple successors .
Graphs are very useful structure . They can be used to solve complex routing problems ,such as :
* designing and routing airlines among the air ports they serve .
* route messages over a computer network from one node to another .

3. Terminology Graph collection of nodes (vertices)
collection of line segments connecting vertices (edges)
Graph may be :
Directed
Each line segment has a direction (Arc) to its successor
Undirected
No direction on any line segment (Edge)

5. Neighbors
Two vertices are said to be neighbors if an edge directly connects them
Path
A sequence of vertices in which each vertex is adjacent to the other
Cycle
A path that start and ends with the same vertex
Loop
A single Arc that begins and ends with the same vertex

6. Strongly connected
If there is a path from each vertex to every other vertex in the directed graph .
Weakly connected
If at least two vertices are not connected
Disjoint
A graph is disjoint if it not connected

7. Weakly connected A B E G F C D H I

8. Strongly connected A B E G F C D H I

9. Disjoint A B E G F C D H I

10. Degree of vertex
Is the number of lines incident to it .
Out degree of vertex in digraph
Is the number of arcs leaving the vertex
Indegree
Is the number of arcs entering the vertex

11. Operations Add Vertex Insert a new vertex in the graph
When a vertex is added it is disjoint , it is not connected to any other vertices in the list . B A B A
AddVertix C C E E

12. Delete Vertex
Removes a vertex from the graph .When a vertex is deleted , all connecting edges are removed . B A B A C E C E

13. Connect a vertex to a destination vertex .
Add edge
Connect a vertex to a destination vertex .
If the graph is a digraph , then one of the edges must be the source and the other is the destination . B A B A C E C E

14. Find Vertex
Traverse the graph looking for a specified vertex.
If the vertex is found , its data are returned . If it is not founded , an error is indicated .

15. Graph Storage Structures
To represent a graph , we need to store two sets :
The vertices of the graph
The edges or arcs .
The two common structures used to store these sets are array and linked list .

16. Adjacency matrix
Uses a vector ( one –dimensional array ) for the vertices and a matrix (two - dimensional array) to store the edges .

17. Adjacency list
Uses a two- dimensional ragged array to store the edges .
The vertex list is a singly linked list of the vertices in the list .