Princeton Algorithm II-4.1 Undirected Graph

• Basic Concept for Graph

  • self-loop: an edge that connects a vertex to itself
  • parallel: edges: two edges are parallel if they connect the same pair of vertices
  • adjacent: When an edge connects two vertices, we say that the vertices are adjacent to one another and that the edge is incident on both vertices
  • degree: number of edges incident on it
  • subgraph: the subset of a graph's edges that constitutes a graph
  • path: a sequence of vertices connected by edges
  • cycle: a path(at least one edge) whose first and last vertices are the same
  • connected: A graph is connected if there is a path from every vertex to every other vertex.
  • connected components: A graph that is not connected
  • spanning tree: A spanning tree of a connected graph is a subgraph that contains all of the graph's vertices and is a single tree

• Basic Concept for Tree

  • height:
  • depth:
• Graph Representation

//计算v的度数
public static int degree(Graph G, int v) {
    int degree = 0;
    for (int w : G.adj(v)) degree++;
    return degree;
}

public static int maxDegree(Graph G) {
    int max = 0;
    for (int v = 0; v < G.V(); v++) {
        if (degree(G, v) > max) 
            max = degree(G, v);
        return max;
}

public static double avgDegree(Graph G) {
    return 2.0 * G.E() / G.V();
}

• Depth-first search

• Breadth-first search

• Connected Component