有哪些方法可以代表Java中的加权有向图？

Question

I can't use any external libraries, so I'm trying to think of some ways to build the data structure myself. I was thinking maybe something like this:

public class Node{
    Set<Edge> adjacent;
    int value;
}

public class Edge{
    Node target;
    int weight;
}

But I'm guessing there's probably a better way to do it.

My eventual use for this graph is to run the Bellman Ford algorithm on it, but I obviously need a functioning graph first!

Answer 1

The answer depends a lot on the algorithms that you are planning to apply to your graphs.

There are two common ways to represent a graph - an adjacency list and an adjacency matrix . In your case, and adjacency matrix is a square array of integers representing weights. Your representation uses an adjacency list.

There are algorithms that work better on adjacency matrixes (eg Floyd-Warshall algorithm). Other algorithms work better on adjacency lists (eg Dijkstra's algorithm). If your graph is sparse, using adjacency matrix may be prohibitive.

Answer 2

As usual, you can represent graphs as Adjacency Lists or Adjacency Matrices. The choice really depends on the details of your problem.

Using an Adjacency Matrix, you could simply have a matrix of integers, representing the weight.

If you decide to have an Adjacency List, you could simply store a list of list of integers (assuming the nodes of your graph are identified by an integer value), similar to what you've done.

Answer 3

You can use a node as in an unweighted graph, holding a list of nodes to which it is connected,and additionally add the weights associated with the connections as:

public class Node{
    int value;
    HashMap<Node,Integer> adjacency;
}