Question

如何在Matlab中使用0s和1s的对称矩阵找到分离的链接块的数量？

例如，在矩阵A中，如果A（n，m）= 1，则成员n和m连接。连接元素制作块。在下面的矩阵中，成员2,3,4,5,6,8,9连接并形成一个块。此外，有两个大小等于2的簇和一个大小为7的块。

A = [1     0     0     0     0     0     0     0     0     0          
     0     1     1     1     1     1     0     1     1     0
     0     1     1     1     1     1     0     1     1     0
     0     1     1     1     1     1     0     1     1     0
     0     1     1     1     1     1     0     1     1     0
     0     1     1     1     1     1     0     1     1     0
     0     0     0     0     0     0     1     0     0     0
     0     1     1     1     1     1     0     1     1     0
     0     1     1     1     1     1     0     1     1     0
     0     0     0     0     0     0     0     0     0     1]

Answer 1

按照上一个问题（link），您可以使用标签而不是二元指示，然后使用每个街区中的成员数量：

A = false(10);
% direct connections
A(2,3) = 1;
A(3,4) = 1;
A(5,6) = 1;
A(4,9) = 1;
A = A | A';
B = double(A | diag(ones(1,10))); % each node is connected to it self
B(B == 1) = 1:nnz(B); % set initial unique labels
while true
    B_old = B;
    % connect indirect connected nodes
    for node = 1:size(B,1)
        row = B(node,:);
        col = row';
        row = row > 0;
        col(col > 0) = max(col);
        cols = repmat(col,[1 nnz(row)]);
        % set the same label for each group of connected nodes
        B(:,row) = max(B(:,row) , cols);
    end
    if isequal(B,B_old)
        break
    end
end
% get block size
u = unique(B);
counts = hist(B(:),u);
% remove non connections
counts(u == 0) = [];
u(u == 0) = [];
% remove self connections
u(counts == 1) = [];
counts(counts == 1) = [];
% block size
blocksize = sqrt(counts);

矩阵中链接元素的块数

1 个答案: