根据邻接矩阵求有向网络聚集系数matlab

以下是求解有向网络聚集系数的matlab代码：

% 输入邻接矩阵
A = [0 1 1 0 0; 0 0 1 0 0; 0 0 0 1 1; 0 0 0 0 1; 0 0 0 0 0];

% 计算每个节点的入度和出度
indegree = sum(A, 1);
outdegree = sum(A, 2);

% 计算每个节点的聚集系数
clustering_coefficient = zeros(size(A,1),1);
for i=1:size(A,1)
neighbors = find(A(i,:)); % 找到节点i的邻居节点
if length(neighbors) >= 2 % 如果节点i的度数大于等于2
edges = sum(A(neighbors, neighbors)); % 计算邻居节点之间的边数
clustering_coefficient(i) = 2*edges / (length(neighbors)*(length(neighbors)-1));
end
end

% 输出结果
disp('邻接矩阵：');
disp(A);
disp('每个节点的入度：');
disp(indegree);
disp('每个节点的出度：');
disp(outdegree);
disp('每个节点的聚集系数：');
disp(clustering_coefficient);

相关问题

根据邻接矩阵求有向网络聚集系数matlab代码

以下是根据邻接矩阵求有向网络聚集系数的matlab代码：

function ClusteringCoefficient = directedClusteringCoefficient(adjMatrix)
% Calculate the directed clustering coefficient of a network given its adjacency matrix.
% The input adjMatrix is a binary adjacency matrix representing the connections between nodes.
% The output ClusteringCoefficient is a vector of clustering coefficients for each node in the network.

n = size(adjMatrix,1);
ClusteringCoefficient = zeros(n,1);

for i = 1:n
    neighbors = find(adjMatrix(i,:)); % find the neighbors of node i
    k = length(neighbors);
    if k>1 % only consider nodes with at least 2 neighbors
        edges = adjMatrix(neighbors,neighbors); % extract the subgraph formed by the neighbors
        numTriangles = trace(edges^3)/2; % count the number of triangles in the subgraph
        maxTriangles = k*(k-1); % calculate the maximum number of triangles that could be formed
        if maxTriangles > 0 % avoid division by zero
            ClusteringCoefficient(i) = numTriangles / maxTriangles; % calculate the clustering coefficient of node i
        end
    end
end

end

该代码首先遍历每个节点，找到其邻居节点。然后，对于每个有至少两个邻居的节点，它会提取邻居子图并计算其中三角形的数量。最后，该代码将三角形数量除以最大可能的三角形数量，以获得该节点的聚集系数。最终，该代码将聚集系数存储在一个向量中，并返回该向量作为输出。

根据邻接矩阵求有向网络平均最短路径matlab代码

以下是基于邻接矩阵求有向网络平均最短路径的MATLAB代码：

function [avg_shortest_path] = directed_network_shortest_path(adj_matrix)
% Function to calculate the average shortest path of a directed network
% based on its adjacency matrix
% Inputs:
% adj_matrix : n x n adjacency matrix of the network, where n is the number of nodes
% Outputs:
% avg_shortest_path : average shortest path of the network

n = size(adj_matrix, 1); % number of nodes
dist_matrix = zeros(n); % initialize distance matrix

% initialize distance matrix using adjacency matrix
for i = 1:n
for j = 1:n
if adj_matrix(i, j) ~= 0
dist_matrix(i, j) = adj_matrix(i, j);
else
dist_matrix(i, j) = Inf;
end
end
end

% Floyd-Warshall algorithm to calculate all-pairs shortest paths
for k = 1:n
for i = 1:n
for j = 1:n
if dist_matrix(i, k) + dist_matrix(k, j) < dist_matrix(i, j)
dist_matrix(i, j) = dist_matrix(i, k) + dist_matrix(k, j);
end
end
end
end

% calculate average shortest path
avg_shortest_path = sum(sum(dist_matrix(~isinf(dist_matrix)))) / (n*(n-1));

end

使用示例：

% example adjacency matrix
adj_matrix = [0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0; 0 0 0 0 1; 1 0 0 0 0];

% calculate average shortest path
avg_shortest_path = directed_network_shortest_path(adj_matrix);

% display result
fprintf('Average shortest path: %.2f\n', avg_shortest_path);