圖的鄰接表表示法，是為每一個頂點建立一個連結串列，連結串列裡存放著相同弧尾的 弧的資訊，這些連結串列順序存放在陣列中。下面是無向圖g2的鄰接表 

鄰接表 比 鄰接矩陣 節省空間，同時 也帶來一些操作上的 不便，例如 看 兩個頂點是否 相鄰，需要 遍歷 連結串列，在 求 無向圖頂點的度時，只需 遍歷 頂點的連結串列，而 求 有向圖 頂點的度 需要 遍歷 整個圖 查詢 弧頭 為這個頂點的 個數。 如果 不想這樣做，可以 建立 逆鄰接表，即 連結串列裡 存放著 相同 弧頭的 弧 的資訊。 下一節 要說的 十字連結串列 類似於這種結構。

下面 上程式碼：

// Graph.cpp : 定義控制檯應用程式的入口點。
//圖的鄰接表 表示法

#include "stdafx.h"
#include <cstdlib>
#include <climits>
#define MAX_VERTEX_NUM 20
#define INFINITY INT_MAX
enum E_Graph_Kind  
{  
    DG = 0,//有向圖  
    DN,//有向網  
    UDG,//無向圖  
    UDN,//無向網  
};  
struct ArcNode//邊（弧）
{
	int adjVex;//頂點在陣列中的位置
	ArcNode * nextAdj;
	int weight;//權值
};

typedef struct VNode//頂點
{
	ArcNode * head;//頭指標
	char vexName;//頂點名稱
}AdjList[MAX_VERTEX_NUM];
struct Graph//圖
{
	AdjList list;//鄰接表
	int arcNum,vexNum;
	E_Graph_Kind kind;
};

//頂點在陣列中的位置
int vexLocation(Graph g,char vex){
	for (int i = 0; i < g.vexNum; i++){
		if (g.list[i].vexName == vex){
			return i;
		}
	}
	return -1;
}

ArcNode * getHeadNode(){//獲得頭節點..
	ArcNode * node = (ArcNode*)malloc(sizeof(ArcNode));
	if (node != NULL){
		node->adjVex = -1;
		node->nextAdj = NULL;
		node->weight = INFINITY;
	}
	return node;
}

ArcNode * getArcNode(Graph g,char vexName){
	ArcNode * node = getHeadNode();
	if (node != NULL){
		int location = vexLocation(g,vexName);
		node->adjVex = location;
	}
	return node;
}

void createDG(Graph * graph);  
void createDN(Graph * graph);  
void createUDG(Graph * graph);  
void createUDN(Graph * graph);  
  
void graphCreate(Graph * graph){  
    E_Graph_Kind kind;  
    printf("請輸入要建立的圖的型別（有向圖：0，有向網：1，無向圖：2，無向網：3）\n");  
    scanf("%d",&kind);  
    switch (kind){  
    case DG:  
        createDG(graph);  
        break;  
    case DN:  
        createDN(graph);  
        break;  
    case UDG:  
        createUDG(graph);  
        break;  
    case UDN:  
        createUDN(graph);  
        break;  
    default:  
        break;  
    }  
} 

//有向圖
void createDG(Graph * g){
	g->kind = DG;
	printf("輸入圖的頂點樹 和 邊（弧）樹\n");
	scanf("%d%d%*c",&g->vexNum,&g->arcNum);  
    //構造頂點集  
    printf("請輸入頂點集\n");  
    for (int i = 0; i < g->vexNum; i++){  
        char name;
		scanf("%c",&name);
		g->list[i].vexName = name;
		g->list[i].head = getHeadNode();//頭指標指向頭節點.
    }  
    //構造頂點關係  
    fflush(stdin);  
    printf("請輸入頂點的關係\n");  
    for (int i = 0; i < g->arcNum; i++){  
        char vex1,vex2;  
        scanf("%c%c%*c",&vex1,&vex2);  
		int location1 = vexLocation(*g,vex1);    
		ArcNode * node = getArcNode(*g,vex2);
		node->nextAdj = g->list[location1].head->nextAdj;
		g->list[location1].head->nextAdj = node;
    }  
}
//有向網..
void createDN(Graph * g){
	g->kind = DN;
	printf("輸入圖的頂點樹 和 邊（弧）樹\n");
	scanf("%d%d%*c",&g->vexNum,&g->arcNum);  
    //構造頂點集  
    printf("請輸入頂點集\n");  
    for (int i = 0; i < g->vexNum; i++){  
        char name;
		scanf("%c",&name);
		g->list[i].vexName = name;
		g->list[i].head = getHeadNode();
    }  
    //構造頂點關係  
    fflush(stdin);  
    printf("請輸入頂點的關係\n");  
    for (int i = 0; i < g->arcNum; i++){  
        char vex1,vex2;
		int weight;
		scanf("%c%c%d%*c",&vex1,&vex2,&weight);  
		int location1 = vexLocation(*g,vex1);
		ArcNode * node = getArcNode(*g,vex2);
		node->weight = weight;
		node->nextAdj = g->list[location1].head->nextAdj;
		g->list[location1].head->nextAdj = node;
    }  
}
//無向圖
void createUDG(Graph * g){
	g->kind = UDG;
	printf("輸入圖的頂點樹 和 邊（弧）樹\n");
	scanf("%d%d%*c",&g->vexNum,&g->arcNum);  
    //構造頂點集  
    printf("請輸入頂點集\n");  
    for (int i = 0; i < g->vexNum; i++){  
        char name;
		scanf("%c",&name);
		g->list[i].vexName = name;
		g->list[i].head = getHeadNode();
    }  
    //構造頂點關係  
    fflush(stdin);  
    printf("請輸入頂點的關係\n");  
    for (int i = 0; i < g->arcNum; i++){  
        char vex1,vex2;
		scanf("%c%c%*c",&vex1,&vex2);  
		int location1 = vexLocation(*g,vex1);
		ArcNode * node1 = getArcNode(*g,vex2);
		node1->nextAdj = g->list[location1].head->nextAdj;
		g->list[location1].head->nextAdj = node1;
		int location2 = vexLocation(*g,vex2);
		ArcNode * node2 = getArcNode(*g,vex1);
		node2->nextAdj = g->list[location2].head->nextAdj;
		g->list[location2].head->nextAdj = node2;
    }  
}
//無向網
void createUDN(Graph * g){
	g->kind = UDN;
	printf("輸入圖的頂點樹 和 邊（弧）樹\n");
	scanf("%d%d%*c",&g->vexNum,&g->arcNum);  
    //構造頂點集  
    printf("請輸入頂點集\n");  
    for (int i = 0; i < g->vexNum; i++){  
        char name;
		scanf("%c",&name);
		g->list[i].vexName = name;
		g->list[i].head = getHeadNode();
    }  
    //構造頂點關係  
    fflush(stdin);  
    printf("請輸入頂點的關係\n");  
    for (int i = 0; i < g->arcNum; i++){  
        char vex1,vex2;
		int weight;
		scanf("%c%c%d%*c",&vex1,&vex2,&weight);  
		int location1 = vexLocation(*g,vex1);
		ArcNode * node1 = getArcNode(*g,vex2);
		node1->weight = weight;
		node1->nextAdj = g->list[location1].head->nextAdj;
		g->list[location1].head->nextAdj = node1;
		int location2 = vexLocation(*g,vex2);
		ArcNode * node2 = getArcNode(*g,vex1);
		node2->weight = weight;
		node2->nextAdj = g->list[location2].head->nextAdj;
		g->list[location2].head->nextAdj = node2;
    }  
}

void graphDestory(Graph * g){
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->list[i].head;
		while (next != NULL){
			ArcNode * freeNode = next;
			next = next->nextAdj;
			free(freeNode);
		}
		g->list[i].head = NULL;
		g->list[i].vexName = ' ';
	}
	g->vexNum = g->arcNum = 0;
}
//vex1 和 vex2是否相鄰..
bool grphIsAdj(Graph g,char vex1,char vex2){
	int location = vexLocation(g,vex1);
	ArcNode * next = g.list[location].head->nextAdj;//第一個節點是頭結點的後繼
	while (next != NULL){
		if (g.list[next->adjVex].vexName == vex2){
			return true;
		}
		next = next->nextAdj;
	}
	return false;
}
//頂點vex的度.
//有向 = 出度 + 入度
//無向 = 出度
int graphDegree(Graph g,char vex){
	int degree = 0;
	int location = vexLocation(g,vex);
	ArcNode * next = g.list[location].head->nextAdj;
	while (next != NULL){//出度
		degree ++;
		next = next->nextAdj;
	}
	if (g.kind == DG || g.kind == DN){
		//有向圖還需要遍歷圖，尋找入度.
		for (int i = 0; i < g.vexNum; i++){
			ArcNode * next = g.list[i].head->nextAdj;
			while (next != NULL){
				if (next->adjVex == location){
					degree ++;
				}
				next = next->nextAdj;
			}
		}
	}
	return degree;
}
//vex 的第一個鄰接點
char firstAdj(Graph g,char vex){
	int location = vexLocation(g,vex);
	ArcNode * next = g.list[location].head->nextAdj;
	if (next != NULL){
		return g.list[next->adjVex].vexName;
	}
	return ' ';
}
//vex1 相對於 vex2 的下一個鄰接點。。。
char nextAdj(Graph g,char vex1,char vex2){
	int location = vexLocation(g,vex1);
	ArcNode * next = g.list[location].head->nextAdj;
	while (next != NULL){//查詢到 vex2
		if (g.list[next->adjVex].vexName == vex2){
			break;
		}
		next = next->nextAdj;
	}
	if (next != NULL){
		ArcNode * nextNode = next->nextAdj;
		if (nextNode != NULL){
			return g.list[nextNode->adjVex].vexName;
		}
	}
	return ' ';
}
//插入頂點
void insertVex(Graph * g,char vex){
	if (g->vexNum < MAX_VERTEX_NUM){
		g->list[g->vexNum].vexName = vex;
		g->list[g->vexNum].head = getHeadNode();
		g->vexNum++;
	}
}
//刪除頂點
void deleteVex(Graph * g,char vex){
	int location = vexLocation(*g,vex);
	//釋放空間
	ArcNode * next = g->list[location].head->nextAdj;
	int delNum = 0;
	while (next != NULL){
		ArcNode * freeNode = next;
		next = next->nextAdj;
		free(freeNode);
		delNum++;
	}
	//vex下面的 頂點上移
	for (int i = location + 1; i < g->vexNum; i++){
		g->list[i-1] = g->list[i];
	}
	g->vexNum --;
	//刪除與頂點vex 相關的邊（弧）(以及更新 所有節點的 adjVex )要遍歷圖..
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->list[i].head->nextAdj;
		ArcNode * pre = g->list[i].head;
		while (next != NULL){
			if (next->adjVex == location){
				ArcNode * freeNode = next;
				next = next->nextAdj;
				pre->nextAdj = next;
				free(freeNode);
				delNum++;
			}
			else {
				if (next->adjVex > location){//在頂點下面的節點位置要減1
					next->adjVex --;
				}
				pre = next;
				next = next->nextAdj;
			}
		}
	}
	g->arcNum -= delNum;//有向
	if (g->kind == UDG || g->kind == UDN){
		g->arcNum += delNum/2;
	}
}
//插入邊（弧）
void insertArc(Graph * g,char vex1,char vex2){
	int location1 = vexLocation(*g,vex1);
	ArcNode * node1 = getArcNode(*g,vex2);
	node1->nextAdj = g->list[location1].head->nextAdj;
	g->list[location1].head->nextAdj = node1;
	//無向圖需要插入另外一邊.
	if (g->kind == UDG || g->kind == UDN){
		int location2 = vexLocation(*g,vex2);
		ArcNode * node2 = getArcNode(*g,vex1);
		node2->nextAdj = g->list[location2].head->nextAdj;
		g->list[location2].head->nextAdj = node2;
	}
	g->arcNum ++;
}
//刪除邊（弧）
void deleteArc(Graph * g,char vex1,char vex2){
	g->arcNum--;
	int location1 = vexLocation(*g,vex1);
	int location2 = vexLocation(*g,vex2);
	ArcNode * next = g->list[location1].head->nextAdj;
	ArcNode * pre = g->list[location1].head;
	while (next != NULL){
		if (next->adjVex == location2){
			pre->nextAdj = next->nextAdj;
			free(next);
			break;
		}
		pre = next;
		next = next->nextAdj;
	}
	if (g->kind == UDG || g->kind == UDN ){//無向圖還需要刪除 另外一邊
		next = g->list[location2].head->nextAdj;
		pre = g->list[location2].head;
		while (next != NULL){
			if (next->adjVex == location1){
				pre->nextAdj = next->nextAdj;
				free(next);
				break;
			}
			pre = next;
			next = next->nextAdj;
		}
	}
}

void printGrahp(Graph g){
	for (int i = 0; i < g.vexNum; i++){
		printf("%c的鄰接點有：",g.list[i].vexName);
		ArcNode * next = g.list[i].head->nextAdj;
		while (next != NULL){
			printf("%c",g.list[next->adjVex].vexName);
			next = next->nextAdj;
		}
		printf("\n");
	}
}


int _tmain(int argc, _TCHAR* argv[])
{
	Graph g;
	graphCreate(&g);
	printGrahp(g);
	printf("圖的頂點數：%d,邊（弧）樹為：%d\n",g.vexNum,g.arcNum);
	char first = firstAdj(g,'a');
	char next = nextAdj(g,'a','c');
	char * isAdj = grphIsAdj(g,'c','d')? "相鄰" : "不相鄰";
	int degree = graphDegree(g,'d');
	printf("a的第一個鄰接點是%c,a的c鄰接點的下一個鄰接點是：%c\n",first,next);
	printf("c 和 d %s,d的度為：%d\n",isAdj,degree);
	insertVex(&g,'e');
	printf("插入e頂點之後圖結構如下：\n");
	printGrahp(g);
	insertArc(&g,'a','e');
	printf("插入(a,e)邊（弧）之後圖結構如下：\n");
	printGrahp(g);
	deleteArc(&g,'d','c');
	printf("刪除(d,c)邊（弧）之後圖結構如下：\n");
	printGrahp(g);
	deleteVex(&g,'a');
	printf("刪除頂點a之後圖結構如下：\n");
	printGrahp(g);
	printf("圖的頂點數：%d,邊（弧）樹為：%d\n",g.vexNum,g.arcNum);
	//及時銷燬記憶體是個好習慣
	graphDestory(&g);
	return 0;
}
 

最後 圖的 頂點樹為 4， 邊（弧） 數 為 1