java - 使用 Java 中的 Floyd Warshall 算法保存图中的最短路径

Question

我正在尝试为 Java 中的无向、未加权(权重 = 1)图编写 Betweeness Centrality 方法。我采用的方法是找到图中的所有最短路径，然后遍历这些路径并计算顶点在该路径中出现的频率。我使用 Floyd Warshall 算法找到最短路径，并使用另一个数组重建路径，类似于 pseudo code on the Wikipedia.

但是，我的结果不正确，我试图找出问题所在，但我做不到。为了完整起见，我将在这里发布整个代码，但是它很困惑，所以我深表歉意。我会评论我认为会出现问题的位。

public void calculateBetweenessCentrality() {
    // Floyd warshall algorithm, storing paths with R
    int noPath = Integer.MAX_VALUE / 4;
    int[][] adjMatrix = getAdjacencyMatrix();
    int distances[][] = new int[numVertices][numVertices];
    int[][] R = new int[numVertices][numVertices];

    // Initialize the arrays, setting "-5000" as null instead. Possible error here?
    for (int i = 0; i < numVertices; i++) {
        for (int j = 0; j < numVertices; j++) {
            if (adjMatrix[i][j] == 0) { 
                distances[i][j] = noPath;
                R[i][j] = -5000; // null
            }
            else {
                distances[i][j] = adjMatrix[i][j];
                R[i][j] = j;
            }

        }
    }
    // Do the algorithm, and save in R, possible error here?
    for (int k = 0; k < numVertices; k++) {
        for (int i = 0; i < numVertices; i++) {
            for (int j = 0; j < numVertices; j++) {
                if (distances[i][j] > distances[i][k] + distances[k][j]) {
                    distances[i][j] = distances[i][k] + distances[k][j];
                    R[i][j] = R[i][k];
                }

            }
        }
    }

    // Go through R and construct the shortest paths, record the frequency for each node (indexs). Possible error here?
    HashMap<Integer, Integer> frequencies = new HashMap<>(); // Key = index, Value = frequency
    for (int i = 0; i < numVertices; i++) {
        for (int j = 0; j < numVertices; j++) {
            ArrayList<Integer> path = findShortestPath(R, i, j);
            for (int p : path) {
                int freq = frequencies.containsKey(p) ? frequencies.get(p) : 0;
                frequencies.put(p, freq + 1);
            }
        }
    }

    HashMap<Integer, Integer> temp = new HashMap<Integer, Integer>(); // Instead of printing the vertex's adjacency matrix index value, get the actual value for displaying purposes.
    for (Entry<Integer, Integer> freq : frequencies.entrySet()) {
        temp.put(verticesIndexValue.get(freq.getKey()), freq.getValue());

    }
    System.out.println("Top 5 nodes: \nNode - Count");
    frequencies.entrySet().stream().sorted(Map.Entry.comparingByValue(Collections.reverseOrder())).limit(5)
            .collect(Collectors.toMap(Map.Entry::getKey, Map.Entry::getValue, (e1, e2) -> e1, LinkedHashMap::new))
            .forEach((node, frequency) -> System.out.println(node + " - " + frequency));

}

private ArrayList<Integer> findShortestPath(int[][] R, int u, int v) {

    ArrayList<Integer> paths = new ArrayList<>();

    if(R[u][v] == -5000)
        return paths;

    paths.add(u);
    while(u != v) {
        u = R[u][v];
        paths.add(u);
    }

    return paths;
}

我正在测试的图表来自 this input here ，其中每条线都是一条边。该 pastebin 中的图形创建了两个连接的组件。我得到的第一个组件的输出如下:

Top 5 nodes: 
Node - Count
11336782 - 11393
50393960 - 9047
627363 - 4079
849131 - 3799
5676102 - 3351

答案其实是50393960是顶级节点。如果有人可以指导我去哪里出错，我将不胜感激。谢谢 =)

Answer 1

您的代码在计算频率的地方包含错误 - 根据介数中心性的定义，在计算特定顶点 V 时，您应该排除以顶点 V 开始或结束的最短路径。基本上这意味着当遍历最短路径时，您不应该将开始和结束顶点添加到频率中。试试这个:

HashMap<Integer, Integer> frequencies = new HashMap<>(); // Key = index, Value = frequency
for (int i = 0; i < numVertices; i++) {
    for (int j = 0; j < numVertices; j++) {
        ArrayList<Integer> path = findShortestPath(R, i, j);
        for (int p : path) {
            if (p == i || p == j) {
               continue;
            }
            int freq = frequencies.containsKey(p) ? frequencies.get(p) : 0;
            frequencies.put(p, freq + 1);
        }
    }
}