请给我一段matlab代码,利用特征向量中心性算法识别复杂网络节点重要度,输入为无向有权网络图的邻接矩阵
时间: 2024-05-12 08:18:37 浏览: 6
Sure, here is a Matlab code for identifying node importance in complex networks using centrality algorithms:
```matlab
% Load the adjacency matrix of the network
A = load('adjacency_matrix.txt');
% Calculate the degree centrality
deg_cen = sum(A, 2);
% Calculate the eigenvector centrality
[eig_vec, eig_val] = eig(A);
[eig_val_sorted, eig_val_sort_idx] = sort(diag(eig_val), 'descend');
top_eig_vecs = eig_vec(:, eig_val_sort_idx(1:10));
eig_cen = sum(abs(top_eig_vecs), 2);
% Calculate the betweenness centrality
num_nodes = size(A, 1);
btw_cen = zeros(num_nodes, 1);
for i = 1:num_nodes
for j = i+1:num_nodes
if A(i,j) == 1
paths = shortestpaths(A, i, j);
num_paths = sum(paths > 0);
shortest_paths = paths(paths > 0) - 1;
btw_cen(i) = btw_cen(i) + sum((1./num_paths) .* (shortest_paths == min(shortest_paths)));
btw_cen(j) = btw_cen(j) + sum((1./num_paths) .* (shortest_paths == min(shortest_paths)));
end
end
end
% Normalize the centralities
deg_cen = deg_cen / (num_nodes - 1);
eig_cen = eig_cen / sum(eig_cen);
btw_cen = btw_cen / ((num_nodes - 1) * (num_nodes - 2) / 2);
% Combine the centralities to get the final node importance score
node_scores = deg_cen + eig_cen + btw_cen;
% Print the node scores in descending order
[node_scores_sorted, node_score_sort_idx] = sort(node_scores, 'descend');
fprintf('Node\tScore\n');
for i = 1:num_nodes
fprintf('%d\t%f\n', node_score_sort_idx(i), node_scores_sorted(i));
end
```
Note that this code calculates three common centrality measures: degree centrality, eigenvector centrality, and betweenness centrality. These measures are then combined to obtain a final node importance score, which represents the relative importance of each node in the network. The code assumes that the adjacency matrix of the network is stored in a file called "adjacency_matrix.txt".