[Function add]

1.Add interface and default method for graph.

Author: Seanforfun

Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/Graph.java

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+package ca.mcmaster.chapter.four.graph;
+
+import java.awt.DisplayMode;
+
+public interface Graph {
+	/**
+	 * @Description: Get the vertex number.
+	 * @return
+	 */
+	public int V();
+	
+	/**
+	 * @Description: Get the edge number.
+	 * @return
+	 */
+	public int E();
+	/**
+	 * @Description: Create an edge between w and v.
+	 * @param v
+	 * @param w
+	 */
+	public void addEdge(int v, int w);
+	/**
+	 * @Description: Get all vertex adjacent to v.
+	 * @param v
+	 * @return
+	 */
+	public Iterable<Integer> adj(int v);
+	
+	/**
+	 * @Description: Return degree of given vertex.
+	 * @param G
+	 * @param V
+	 * @return
+	 */
+	static Integer degree(Graph G, int V){
+		Integer degree = new Integer(0);
+		for(int w : G.adj(V)) degree++;
+		return degree;
+	}
+	
+	/**
+	 * @Description: Find the largest degree in the graph
+	 * @param G
+	 * @param V
+	 * @return
+	 */
+	static int maxDegree(Graph G, int V){
+		int max = 0;
+		for(int w : G.adj(V) )
+			if(w > max)
+				max = w;
+		return max;
+	}
+	
+	/**
+	 * @Description: Calculate the average degree for all vertex.
+	 * @param G
+	 * @return
+	 */
+	static double avgDegree(Graph G){
+		return 2 * G.E() / G.V();
+	}
+	
+	/**
+	 * @Description: Get the number of selt loop.
+	 * @param G
+	 * @param V
+	 * @return
+	 */
+	static int numOfSelfLoop(Graph G, int V){
+		int num = 0;
+		int vNum = G.V();
+		for(int v = 0; v < vNum; v++ )
+			for(int w : G.adj(v))
+				if(w == v)
+					num ++;
+		return num/2;	//w,v and v,w will both be counted.
+	}
+	
+	/**
+	 * @Description: Print a graph.
+	 */
+	default void display(){
+		int vertexNum = this.V();
+		for(int v = 0; v < vertexNum; v++){
+			StringBuilder sb = new StringBuilder(v + " -> ");
+			for(int w : adj(v))
+				sb.append(w + "");
+			System.out.println(sb.toString());
+		}
+	}
+}

DataStructrue/Graph/UndirectedGraph.md

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+# Undirected Graph无向图
+>无向图由边(edge)和顶点(vertex)组成。
+>当两个顶点通过一条边相连时我们称这两个顶点相邻。同时这条边依附于这两个顶点
+>某个顶点的度数为依附它的边的条数。
+
+* 连通图
+>如果从任意一个顶点都存在一条路径到达一个任意顶点，我们称这幅图是连通图
+
+## 图的接口
+```Java
+public interface Graph {
+	/**
+	 * @Description: Get the vertex number.
+	 * @return
+	 */
+	public int V();
+	/**
+	 * @Description: Get the edge number.
+	 * @return
+	 */
+	public int E();
+	/**
+	 * @Description: Create an edge between w and v.
+	 * @param v
+	 * @param w
+	 */
+	public void addEdge(int v, int w);
+	/**
+	 * @Description: Get all vertex adjacent to v.
+	 * @param v
+	 * @return
+	 */
+	public Iterable<Integer> adj(int v);
+	/**
+	 * @Description: Return degree of given vertex.
+	 * @param G
+	 * @param V
+	 * @return
+	 */
+	static Integer degree(Graph G, int V){
+		Integer degree = new Integer(0);
+		for(int w : G.adj(V)) degree++;
+		return degree;
+	}
+	/**
+	 * @Description: Find the largest degree in the graph
+	 * @param G
+	 * @param V
+	 * @return
+	 */
+	static int maxDegree(Graph G, int V){
+		int max = 0;
+		for(int w : G.adj(V) )
+			if(w > max)
+				max = w;
+		return max;
+	}
+	/**
+	 * @Description: Calculate the average degree for all vertex.
+	 * @param G
+	 * @return
+	 */
+	static double avgDegree(Graph G){
+		return 2 * G.E() / G.V();
+	}
+		/**
+	 * @Description: Get the number of selt loop.
+	 * @param G
+	 * @param V
+	 * @return
+	 */
+	static int numOfSelfLoop(Graph G, int V){
+		int num = 0;
+		int vNum = G.V();
+		for(int v = 0; v < vNum; v++ )
+			for(int w : G.adj(v))
+				if(w == v)
+					num ++;
+		return num/2;	//w,v and v,w will both be counted.
+	}
+		/**
+	 * @Description: Print a graph.
+	 */
+	default void display(){
+		int vertexNum = this.V();
+		for(int v = 0; v < vertexNum; v++){
+			StringBuilder sb = new StringBuilder(v + " -> ");
+			for(int w : adj(v))
+				sb.append(w + "");
+			System.out.println(sb.toString());
+	}
+}
+```