Data Strucrures
Graph is a data structure that consists of following two components:
1. A finite set of vertices also called as nodes.
2. A finite set of ordered pair of the form (u, v) called as edge. The pair is ordered because (u, v) is not same as (v, u) in case of a directed graph(di-graph). The pair of the form (u, v) indicates that there is an edge from vertex u to vertex v. The edges may contain weight/value/cost.
Graphs are used to represent many real-life applications: Graphs are used to represent networks. The networks may include paths in a city or telephone network or circuit network. Graphs are also used in social networks like linkedIn, Facebook. For example, in Facebook, each person is represented with a vertex(or node). Each node is a structure and contains information like person id, name, gender and locale.
Following is an example of an undirected graph with 5 vertices.
Following two are the most commonly used representations of a graph.
1. Adjacency Matrix
2. Adjacency List
There are other representations also like, Incidence Matrix and Incidence List. The choice of the graph representation is situation specific. It totally depends on the type of operations to be performed and ease of use.
Adjacency Matrix:
Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. Adjacency matrix for undirected graph is always symmetric. Adjacency Matrix is also used to represent weighted graphs. If adj[i][j] = w, then there is an edge from vertex i to vertex j with weight w.
The adjacency matrix for the above example graph is:
Pros: Representation is easier to implement and follow. Removing an edge takes O(1) time. Queries like whether there is an edge from vertex ‘u’ to vertex ‘v’ are efficient and can be done O(1).
Cons: Consumes more space O(V^2). Even if the graph is sparse(contains less number of edges), it consumes the same space. Adding a vertex is O(V^2) time.
Adjacency List:
An array of lists is used. Size of the array is equal to the number of vertices. Let the array be array[]. An entry array[i] represents the list of vertices adjacent to the ith vertex. This representation can also be used to represent a weighted graph. The weights of edges can be represented as lists of pairs. Following is adjacency list representation of the above graph.
Pros: Saves space O(|V|+|E|) . In the worst case, there can be C(V, 2) number of edges in a graph thus consuming O(V^2) space. Adding a vertex is easier.
Cons: Queries like whether there is an edge from vertex u to vertex v are not efficient and can be done O(V).
Implementation:
Following code show implementation of graph using Adjacency Matrix
#include<stdio.h>
#include<stdlib.h>
#define max 20
void create_graph();
void display_graph();
void delete_node(char u);
void indegree();
void outdegree();
int adj[max][max];
int n;
int main()
{
int choice;
int node;
while (1)
{
printf("\n1.Create Graph");
printf("\n2.Display Graph");
printf("\n3.Indegree");
printf("\n4.Out Degree");
printf("\n5.Delete a node from Graph");
printf("\n0.Exit");
printf("\nEnter your choice : ");
scanf("%d", &choice);
switch (choice)
{
case 1:
create_graph();
break;
case 2:
display_graph();
break;
case 3:
indegree();
break;
case 4:
outdegree();
break;
case 5:
printf("Enter a node to be deleted : ");
fflush(stdin);
scanf("%d", &node);
delete_node(node);
break;
case 0:
exit(0);
break;
default:
printf("Wrong choice\n");
break;
}
}
return(0);
}
void create_graph()
{
int i, max_edges, source, destination;
printf("Enter number of nodes : ");
scanf("%d", &n);
max_edges = n * (n - 1);
for (i = 1; i <= max_edges; i++)
{
printf("Enter edge %d( 0 0 ) to quit : ", i);
scanf("%d %d", &source, &destination);
if ((source == 0) && (destination == 0))
break;
if (source > n || destination > n || source <= 0 || destination <= 0)
{
printf("Invalid edge!\n");
i--;
}
else
adj[source][destination] = 1;
}
}
void display_graph()
{
int i, j;
for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
printf("%4d", adj[i][j]);
}
printf("\n");
}
}
void delete_node(char u)
{
int i, j;
if(n==0)
{
printf("Graph is empty\n");
return;
}
if(u>n)
{
printf("This node is not present in the graph\n");
return;
}
for(i=u;i<=n-1;i++)
{
for(j=1;j<=n;j++)
{
adj[j][i]=adj[j][i+1];
adj[i][j]=adj[i+1][j];
}
}
n--;
}
void indegree()
{
int i,j,sum=0;
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
sum+=adj[i][j];
printf("\nV%d : %d",i+1,sum);
}
}
void outdegree()
{
int i,j,sum=0;
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
sum+=adj[j][i];
printf("\nV%d : %d",i+1,sum);
}
}
/*
Output:
harish@harish-Inspiron-3537:~/harish/ds$ gcc adj_matrix.c
harish@harish-Inspiron-3537:~/harish/ds$ ./a.out
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice : 1
Enter number of nodes : 3
Enter edge 1( 0 0 ) to quit : 1 2
Enter edge 2( 0 0 ) to quit : 2 3
Enter edge 3( 0 0 ) to quit : 3 1
Enter edge 4( 0 0 ) to quit : 0 0
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice : 2
0 1 0
0 0 1
1 0 0
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice : 3
V1 : 0
V2 : 1
V3 : 1
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice : 4
V1 : 0
V2 : 0
V3 : 1
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice : 5
Enter a node to be deleted : 3
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice : 2
0 1
0 0
1.Create Graph
2.Display Graph
3.Indegree
4.Out Degree
5.Delete a node from Graph
0.Exit
Enter your choice :
*/