Java - Graph的最佳实现结构是什么？

Question

The graph is very large but undirected. Edges are unweighted.

In my implementation, I have to find the vertex with max degree and do deletion on both vertexes and edges.

Linked list? ArrayList? Map?

Which one is better for my implementation?

Answer 1

The two fundamental data structures for representing graphs are the

• adjacency list

• the adjacency matrix

see http://en.wikipedia.org/wiki/Adjacency_list and http://en.wikipedia.org/wiki/Adjacency_matrix .
The articles also discuss the pros and cons of those two structures.

Answer 2

My suggestion would be to store the vertexes in a priority queue. That way you can have very fast access to the vertex with the highest degree. As for how to implement the vertexes, I would store each neighboring vertex in some kind of set data-structure such as a HashSet or a TreeSet to be able to remove stuff efficiently. I wouldn't represent the edges explicitly, it's not needed.

Code, something along the lines of:

class Graph {

  PriorityQueue<Vertex> vertexes;

  public Graph() {
    vertexes = new PriorityQueue<Vertex>(10,new Vertex());
  }

  public Vertex maxDegreeVertex() {
    return vertexes.peek();
  }

  ...

}

class Vertex implements Comparator<Vertex> {
  HashSet<Vertex> edges;

  public Vertex() {
    edges = new HashSet<Vertex>();
  }

  public compare(Vertex v1, Vertex v2) {
    v2.edges.size().compareTo(v1.edges.size());
  }

  ...

}

Hope this helps.

Answer 3

From the above suggested the answer would be

Map with LinkedList...

Your datastructure could be like this(varies according to your requirement)...

Map<?, List<?>>
<Node-name, List-of-nodes-connected-to-it>

Basically, Graphs are best implemented with the help of HASHING and the above datastructure helps a lot in that..

Answer 4

If your algorithm requires looking up on max degree, then you want a data structure ordered by degree, something like a PriorityQueue would be good.

Then you need to store the graph itself. For deletion quickly I'd recommend something like a Sparse Array structure. If you have to use java.util data structures, then a HashMap from vertexes to the list of connected vertexes offers O(1) deletion.

If you could use 3rd party libraries, then there are a list of answers here of which JGraph and JUNG seem most popular.

Answer 5

Graph implementation depends on what you going to do with it. But for most cases Adjacency list based implementation helps.

In Java you can do it using a Map<>. Here is generic Adjacency List based Graph.Java implementation on my blog.

Answer 6

您还可以查看专门设计的库，例如JUNG

Answer 7

Depends on what other requirements you have. A naive, simple approach could be

class Node
{
  List<Node> edges;
  int id;
}

where you'd have a List of all the nodes in the graph. The problem is this can become inconsistent; eg node A might be in node B's edges list, but node B might not be in node A's list. To get around this, you could model it as such:

class Edge
{
  Node incidentA;
  Node incidentB;
}

class Node
{
  int id;
}

Again, you'd have List and List of all the edges and nodes in the system. Of course analyzing this data structure would be done in a very different way than in the other approach.

Answer 8

    public class Graph {
    private Set<Vertex>vertices;
    private Set<Edge>edges;
    private Map<Vertex,List<Edge>>adj;
    // Getter setter



    public Graph(Set<Vertex> vertices, Set<Edge> edges, Map<Vertex, List<Edge>> adj) {
        super();
        this.vertices = vertices;
        this.edges = edges;
        this.adj = adj;
    }
}

// Vertex class
public class Vertex {
    private String name;

    public Vertex(String name) {
        super();
        this.name = name;
    }


}

// Edge class 

public class Edge {
    private Vertex from;
    private Vertex to;
    private int weight;

    public Edge(Vertex from, Vertex to,int weight) {
        super();
        this.from = from;
        this.to = to;
        this.weight = weight;
    }


}

// Driver class 

import java.util.HashSet;
import java.util.Set;

public class Test {
    public static void  main(String[]args) {
        Graph gr = new Graph();
        Vertex a = new Vertex("a");
        Vertex b = new Vertex("b");
        Vertex c = new Vertex("c");
        Vertex d = new Vertex("d");
        Vertex e = new Vertex("e");
        Vertex f = new Vertex("f");
        Vertex g = new Vertex("g");


        Set<Vertex>vertices = gr.getVertices();
        if(vertices == null){
            vertices  = new HashSet<>();
            vertices.add(a);
            vertices.add(b);
            vertices.add(c);
            vertices.add(d);
            vertices.add(e);
            vertices.add(f);
            vertices.add(g);
        }

        Edge ae = new Edge(a, e, 3);        
        Edge ac = new Edge(a, c, 1);
        Edge cf = new Edge(c, f, 9);
        Edge cd = new Edge(c, d, 4);
        Edge eb = new Edge(e, b, 2);
        Edge bd = new Edge(b, d, 5);
        Edge df = new Edge(d, f, 7);

    Set<Edge>edges = gr.getEdges();
    if(edges == null){
        edges = new HashSet<Edge>();
        edges.add(ae);
        edges.add(ac);
        edges.add(cf);
        edges.add(cd);
        edges.add(eb);
        edges.add(bd);
        edges.add(bd);
    }
        gr.setVertices(vertices);
        gr.setEdges(edges);

    }

}