有一个BA无标度网络,邻接矩阵为a1,每条边的流量矩阵为f1,节点编号和节点坐标xyz保存在txt文件node_coordinates.txt中。如何通过计算网络的连通介数中心性找出该网络前十个重要节点?matlab实现且不要用现有函数和库,不要用load函数,不要出现超出索引超出数组范围
时间: 2023-11-28 07:49:58 浏览: 33
以下是MATLAB代码实现:
```matlab
% 读取邻接矩阵和流量矩阵
fid = fopen('adj_matrix.txt', 'r');
a1 = fscanf(fid, '%d');
fclose(fid);
a1 = reshape(a1, [], length(a1)^0.5);
fid = fopen('flow_matrix.txt', 'r');
f1 = fscanf(fid, '%d');
fclose(fid);
f1 = reshape(f1, [], length(f1)^0.5);
% 读取节点坐标
fid = fopen('node_coordinates.txt', 'r');
node_coords = zeros(length(a1), 3);
for i=1:length(a1)
coords = fscanf(fid, '%f', 3);
node_coords(i,:) = coords';
end
fclose(fid);
% 计算网络连通介数中心性
n = length(a1);
bc = zeros(n, 1);
for s=1:n
% 初始化
queue = [];
dist = -1 * ones(n, 1);
sigma = zeros(n, 1);
sigma(s) = 1;
dist(s) = 0;
queue(end+1) = s;
% BFS
while ~isempty(queue)
v = queue(1);
queue = queue(2:end);
for w=find(a1(v,:))
if dist(w) < 0
queue(end+1) = w;
dist(w) = dist(v) + 1;
end
if dist(w) == dist(v) + 1
sigma(w) = sigma(w) + sigma(v);
end
end
end
% 计算介数中心性
delta = zeros(n, 1);
while ~isempty(queue)
w = queue(end);
queue = queue(1:end-1);
for v=find(a1(:,w))'
if dist(v) == dist(w) - 1
delta(v) = delta(v) + (sigma(v) / sigma(w)) * (1 + delta(w));
end
end
if w ~= s
bc(w) = bc(w) + delta(w) * f1(s,w);
end
end
end
% 找出前十个重要节点
[~, idx] = sort(bc, 'descend');
disp('Top 10 important nodes:');
for i=1:10
fprintf('%d. Node %d, (%.2f, %.2f, %.2f)\n', i, idx(i), node_coords(idx(i),:));
end
```
其中,`adj_matrix.txt`和`flow_matrix.txt`分别是邻接矩阵和流量矩阵的文本文件,每行数字之间用空格隔开。`node_coordinates.txt`是节点坐标的文本文件,每行三个数字分别表示节点的$x$、$y$、$z$坐标。
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