数据结构（图）——简单无向图的邻接矩阵，实现广度优先遍历

图有两种表示方法：邻接矩阵和l邻接表，这里使用java实现一个简单的邻接矩阵。
来个栗子尝一尝：

使用邻接矩阵来表示该图
首先定义顶点数组，以及二维数组代表邻接矩阵：

    private int MAXVEX = 0;//顶点个数，顶点数组长度
    private VertexArray<T>[] vertexArray = null;//顶点数组
    private int[][] adjacencyArray = null;//邻接矩阵
 /**
     * 内部类，自定义顶点类型
     *
     * @param <T>
     */
    private class VertexArray<T> {
        private T vertexDate = null;//数据域
        private boolean visited = false;//标记顶点是否访问过

       //此处省略get，set方法
    }

通过构造方法初始化顶点数组及邻接矩阵

/**
     * 构造方法初始化顶点数组，邻接矩阵
     *
     * @param vertexArray
     */
    public AdjacencyMatrix(T[] vertexArray) {
        this.MAXVEX = vertexArray.length;
        this.vertexArray = new VertexArray[MAXVEX];
        this.adjacencyArray = new int[MAXVEX][MAXVEX];
        for (int i = 0; i < MAXVEX; i++) {
            this.vertexArray[i] = new VertexArray<T>();
            this.vertexArray[i].setVertexDate(vertexArray[i]);
            for (int j = 0; j < MAXVEX; j++) {
                this.adjacencyArray[i][j] = 0;
            }
        }
    }

利用二维数组传入各顶点之间的边关系：

 /**
     * 二维数组传入边关系
     */
    public boolean buildMatrix(T[][] side) {
        boolean state = false;
        int p1 = -1;
        int p2 = -1;
        for (int i = 0; i < side.length; i++) {
            p1 = getPosition(side[i][0]);
            p2 = getPosition(side[i][1]);
            if (p1 != -1 && p2 != -1) {
                this.adjacencyArray[p1][p2] = 1;
                this.adjacencyArray[p2][p1] = 1;
                if (!state) state = true;
            }
        }
        return state;
    }

    /**
     * 返回顶点位置
     */
    private int getPosition(T vertex) {
        for (int i = 0; i < MAXVEX; i++) {
            if (vertex.equals(this.vertexArray[i].getVertexDate())) {
                return i;
            }
        }
        return -1;
    }

广度优先遍历（利用栈实现遍历）：

   /**
     * 广度优先遍历
     */
    public void BFS() {
        Queue<VertexArray> queue = new LinkedList<VertexArray>();
        for (int i = 0; i < MAXVEX; i++) {
            if (!this.vertexArray[i].getVisited()) {
                queue.offer(this.vertexArray[i]);
                this.vertexArray[i].setVisited(true);
                System.out.println(this.vertexArray[i].getVertexDate());
                while (queue.size() != 0) {
                    queue.poll();
                    for (int j = 0; j < MAXVEX; j++) {
                        if (this.adjacencyArray[i][j] == 1 && !this.vertexArray[j].getVisited()) {
                            queue.offer(this.vertexArray[j]);
                            this.vertexArray[j].setVisited(true);
                            System.out.println(this.vertexArray[j].getVertexDate());
                        }
                    }
                }
            }
        }
    }

测试代码：

public class AdjacencyMatrixTest {
    public static void main(String[] args) {
        String[] ver = {"v0", "v1","v2","v3","v4","v5"};
        AdjacencyMatrix<String> adj=new AdjacencyMatrix<String>(ver);
        boolean state=adj.buildMatrix(new String[][]{
                {"v0","v1"},
                {"v0","v2"},
                {"v0","v3"},
                {"v1","v2"},
                {"v1","v4"},
                {"v2","v3"},
                {"v3","v4"},
                {"v4","v5"}
        });
        System.out.println(state);
        adj.BFS();
    }
}