Adjacency matrix and adjacency table structure of C ＃ realization graph

In this paper, C# Adjacency matrix and adjacency table structure of realization graph .
The logical structure is divided into two parts ：V and E aggregate , among ,V Is the vertex. ,E Is the edge . therefore , Use a one-dimensional array to store all vertex data in the graph ; Use a two-dimensional array to store the relationship between vertices （ Edge or arc ） The data of , This two-dimensional array is called adjacency matrix . Adjacency matrix is divided into directed graph adjacency matrix and undirected graph adjacency matrix
Adjacency matrix （Adjacency Matrix） Is a matrix representing the adjacency relationship between vertices . set up G=(V,E) It's a picture , among V={v1,v2,…,vn} [1] .G The adjacency matrix of is a matrix with the following properties n Square matrix ：
① For undirected graphs , Adjacency matrix must be symmetric , And the main diagonal must be zero （ Only undirected simple graphs are discussed here ）, The sub diagonal is not necessarily 0, This is not necessarily the case for directed graphs .
② In the undirected graph , Any vertex i It's the third degree i Column （ Or the first i That's ok ） The number of all non-zero elements , In a directed graph, vertices i The output of is the i The number of all non-zero elements in the row , And the penetration is the second i The number of all non-zero elements of the column .
③ Representation of graph common needs by adjacency matrix method n^2 Space , Because the adjacency matrix of an undirected graph must have symmetry , So after deducting that the diagonal is zero , You only need to store the data of the upper triangle or the lower triangle , So just n（n-1）/2 Space .

Adjacency list , The storage method is similar to the child chain representation of a tree , It is a storage structure combining sequential allocation and chain allocation . If the vertex corresponding to this header node has adjacent vertices , Then the adjacent vertices are placed in order in the list that the header points to .
For undirected graphs , Using adjacency table for storage will also lead to data redundancy , Header node A There is a point in the linked list C At the same time , Header node C The linked list will also have a point to A Table node . [1]

The program code is as follows ：
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace The storage structure of the graph
{
using VertexType = System.Char;// Vertex data type alias declaration
using EdgeType = System.Int16;// Data type alias declaration of edge weight in weighted graph
class Program
{
public const int MAxVertexNum =100;// The maximum number of vertices

    static void Main(string[] args)
    {
    }
    /// <summary>
    ///  Definition of graph -- Adjacency matrix 
    /// </summary>
    public struct MGraph {
        public VertexType[] vex;// Vertex table array 
        public EdgeType[][] Edge;// Adjacency matrix 、 Side table 
        public int vexnum,arcnum;// The current vertex and arc number of a graph 
    }
    /// <summary>
    ///  Definition of graph -- Adjacency table method 
    /// </summary>
    public class ArcNode {// Edge table node 
       public int adjvex;
       public  ArcNode next;
    }
    public class VNode {  // Vertex table node 
        VertexType data;// Vertex information 
        ArcNode first;// Just think of the pointer to the first arc attached to the vertex 
    }
    public class ALGraph {
        VNode[] vertices;   // Adjacency list 
        int vexnum, arcnum;// The number of vertices and arcs of a graph 
    }





}

}