Adjacency matrix representation of weighted undirected graph (implemented in C language)
1, Adjacency matrix representation
Definition: the socalled adjacency matrix storage refers to using a onedimensional array to store the information of vertices in the graph, and a twodimensional array to store the information of edges in the graph (i.e. the adjacency relationship between vertices). The twodimensional array storing the adjacency relationship between vertices is called adjacency matrix.
For weighted graphs, if there are edges connected between vertices Vi and Vj, the corresponding term in the adjacency matrix stores the weight corresponding to the edge. If vertices Vi and Vj are not connected, 0 or ∞ is used to represent that there is no edge between the two vertices.
For example, for the following diagram:
We can get its adjacency matrix:
Note: 0, 1, 2 and 3 in brackets represent the subscript of its twodimensional array.
It is easy to find that the weighted adjacency matrix has the following characteristics: ① it is symmetrical about the main diagonal elements; ② The value at the corresponding position of non0 is the weight of the edge.
If there is no weight, the corresponding position of the edge is 1 and the position of the edge is 0. It is also symmetrical about the main diagonal element.
2, Functions realized by this program

Create adjacency matrix of undirected graph

Adjacency matrix corresponding to output undirected graph

Output vertex set

Judge whether the two vertices are adjacent, that is, whether there are directly connected edges
3, Structure definition of weighted undirected graph
typedef char VertexType; //Data type of vertex typedef int EdgeType; //Data types of edge weights in Weighted Graphs typedef struct { VertexType Vex[MaxVertexNum]; //The vertex table MaxVertexNum is the maximum number of vertices, the same below EdgeType Edge[MaxVertexNum][MaxVertexNum];//Adjacency matrix, edge table int vexnum, arcnum; //The current number of vertices and edges of a graph }MGraph;//Weighted undirected graph based on adjacency matrix method
4, Create undirected graph and adjacency matrix
Since it is relatively simple, there is no more explanation. It is worth noting that we should make good use of the symmetry of the adjacency matrix of an undirected graph about the main diagonal, so when inputting the edge weight, we only need to input the upper triangle or the lower triangle.
void CreateMGraph(MGraph *G) { int i,j,k,w; //First determine the number of vertices and edges printf("Please enter the number of vertices and edges,Separated by spaces:\n"); scanf("%d %d",&G>vexnum,&G>arcnum); fflush(stdin);//Empty the input buffer, otherwise the input may not be read normally //Enter values for vertices in turn printf("Please enter the values of the vertices in turn:\n"); for(int i = 0;i < G>vexnum; i++) { printf("Input No%d Vertex information:\n",i+1); scanf("%c",&G>Vex[i]); //The received values are placed in the vertex table fflush(stdin);//Empty the input buffer, otherwise the input may not be read normally } //Initialize adjacency matrix for(i = 0;i < G>vexnum; i++) for(j = 0;j <G>vexnum; j++) G>Edge[i][j] = 0;//It is initialized to 0 at the beginning, or ∞ can be used //Adjacency Matrix Building for (k = 0; k < G>arcnum; k++) { printf("Input edge<vi,vj>Subscript of i,subscript j And right w:\n"); scanf("%d%d%d", &i, &j, &w); //Enter the weight w on the edge < VI, VJ > G>Edge[i][j] = w; G>Edge[j][i] = G>Edge[i][j]; //The undirected graph matrix is symmetric } }
5, Output adjacency matrix
The essence is to traverse a twodimensional array.
//Output adjacency matrix void PrintMatrix(MGraph G) { int i,j; printf("The adjacency matrix is represented as follows:\n"); for (i = 0; i < G.vexnum; i++) { for (j = 0; j < G.vexnum; j++) printf("%10d", G.Edge[i][j]);//Left aligned output printf("\n"); } }
6, Output vertex set
The essence is to traverse a onedimensional array.
//Output vertex set void PrintVex(MGraph G) { printf("\n The vertex set is:"); for(int i=0;i<G.vexnum;i++) printf("%c ",G.Vex[i]); printf("\n"); }
7, Judge whether two vertices are adjacent
The received parameter is the value of two vertices, so you need to find its subscript in the vertex table, and then judge whether the value of the adjacency matrix at its corresponding position is greater than 0. If it is greater than 0, it means adjacency, otherwise it is not adjacency.
Note: if the subscript operation of finding vertices is frequent, it can be encapsulated into a function.
//Judge whether two vertices are adjacent bool Is_Edge_Exist(MGraph G, VertexType d1, VertexType d2) { int i,j,k; for(k=0;k<G.vexnum;k++) { if(G.Vex[k]==d1) i = k;//Find the subscript corresponding to the vertex if(G.Vex[k]==d2) j = k;//Find the subscript corresponding to the vertex } return G.Edge[i][j]>0?1:0; }
8, All codes
#include<stdio.h> #define MaxVertexNum 10 / / maximum number of vertices #Include < stdpool. H > / / according to C99 standard, C language uses bool type and needs to add this header file typedef char VertexType; //Data type of vertex typedef int EdgeType; //Data types of edge weights in Weighted Graphs typedef struct { VertexType Vex[MaxVertexNum]; //Vertex table EdgeType Edge[MaxVertexNum][MaxVertexNum];//Adjacency matrix, edge table int vexnum, arcnum; //The current number of vertices and edges of a graph }MGraph;//Weighted undirected graph based on adjacency matrix method void CreateMGraph(MGraph *G) { int i,j,k,w; //First determine the number of vertices and edges printf("Please enter the number of vertices and edges,Separated by spaces:\n"); scanf("%d %d",&G>vexnum,&G>arcnum); fflush(stdin);//Empty the input buffer, otherwise the input may not be read normally //Enter values for vertices in turn printf("Please enter the values of the vertices in turn:\n"); for(int i = 0;i < G>vexnum; i++) { printf("Input No%d Vertex information:\n",i+1); scanf("%c",&G>Vex[i]); //The received values are placed in the vertex table fflush(stdin);//Empty the input buffer, otherwise the input may not be read normally } //Initialize adjacency matrix for(i = 0;i < G>vexnum; i++) for(j = 0;j <G>vexnum; j++) G>Edge[i][j] = 0;//It is initialized to 0 at the beginning, or ∞ can be used //Adjacency Matrix Building for (k = 0; k < G>arcnum; k++) { printf("Input edge<vi,vj>Subscript of i,subscript j And right w:\n"); scanf("%d%d%d", &i, &j, &w); //Enter the weight w on the edge < VI, VJ > G>Edge[i][j] = w; G>Edge[j][i] = G>Edge[i][j]; //The undirected graph matrix is symmetric } } //Output adjacency matrix void PrintMatrix(MGraph G) { int i,j; printf("The adjacency matrix is represented as follows:\n"); for (i = 0; i < G.vexnum; i++) { for (j = 0; j < G.vexnum; j++) printf("%10d", G.Edge[i][j]);//Left aligned output printf("\n"); } } //Output vertex set void PrintVex(MGraph G) { printf("\n The vertex set is:"); for(int i=0;i<G.vexnum;i++) printf("%c ",G.Vex[i]); printf("\n"); } //Judge whether two vertices are adjacent bool Is_Edge_Exist(MGraph G, VertexType d1, VertexType d2) { int i,j,k; for(k=0;k<G.vexnum;k++) { if(G.Vex[k]==d1) i = k;//Find the subscript corresponding to the vertex if(G.Vex[k]==d2) j = k;//Find the subscript corresponding to the vertex } return G.Edge[i][j]>0?1:0; } int main() { MGraph G;//Undirected graph CreateMGraph(&G);//Create diagram PrintMatrix(G);//Output adjacency matrix PrintVex(G);//Output vertex //Judge whether two vertices are adjacent VertexType d1,d2; d1 = 'A'; d2 = 'B'; if(Is_Edge_Exist(G,d1,d2)) printf("\n%c and%c Adjacency!\n",d1,d2); else printf("\n%c and%c Non adjacency!\n",d1,d2); d2 = 'C'; if(Is_Edge_Exist(G,d1,d2)) printf("\n%c and%c Adjacency!\n",d1,d2); else printf("\n%c and%c Non adjacency!\n",d1,d2); return 0; }
9, Testing
Input example:
When inputting, you only need to input the upper triangular part or the lower triangular part (excluding those on the main diagonal).