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typicalLaplacian.m
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typicalLaplacian.m
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% typical laplacian matrices
L3=[1 -1 0;
-1 2 -1;
0 -1 1];
L4=[1 -1 0 0;
-1 2 -1 0;
0 -1 2 -1;
0 0 -1 1];
L4r=[1 -1 0 0;
-1 3 -1 -1;
0 -1 1 0;
0 -1 0 1];
L1way= ...
[ 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 0 0 2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 0 2 0 0 0 0 0 -1 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1];
L2=[ 6 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 0 0 7 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 0 7 -1 -1 -1 -1 -1 -1 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 6 -1 -1 -1 -1 -1;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1];
Lshu20=[2 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;
-1 3 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 3 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 -1 0 3 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0;
0 -1 0 0 3 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0;
0 0 -1 0 0 3 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0;%row 6?
0 0 -1 0 0 0 3 0 0 0 0 0 0 -1 -1 0 0 0 0 0;
0 0 0 -1 0 0 0 3 0 0 0 0 0 0 0 -1 -1 0 0 0;
0 0 0 -1 0 0 0 0 3 0 0 0 0 0 0 0 0 -1 -1 0;
0 0 0 0 -1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 -1;% row?10
0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 -0 0 0 0 0 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0;%row 15
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0;
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0;
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0;
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1;
];% 树形20个节点双向结构?
Lshu21=[
2 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;
-1 2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;
-1 0 3 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 -1 0 3 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 -1 0 3 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0;
0 0 -1 0 0 3 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0;
0 0 0 -1 0 0 3 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0;%row 6?
0 0 0 -1 0 0 0 3 0 0 0 0 0 0 -1 -1 0 0 0 0 0;
0 0 0 0 -1 0 0 0 3 0 0 0 0 0 0 0 -1 -1 0 0 0;
0 0 0 0 -1 0 0 0 0 3 0 0 0 0 0 0 0 0 -1 -1 0;
0 0 0 0 0 -1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 -1;% row?10
0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 -0 0 0 0 0 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0;%row 15
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0;
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0;
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0;
0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1;
];% 树形21个节点双向结构?
% 21-node tree, same as Lshu21, but Node 1 (root) fails
Lshu21_n1F=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
0,-1,3,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
0 -1 0 3 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 -1 0 3 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0;
0 0 -1 0 0 3 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0;
0 0 0 -1 0 0 3 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0;%row 6?
0 0 0 -1 0 0 0 3 0 0 0 0 0 0 -1 -1 0 0 0 0 0;
0 0 0 0 -1 0 0 0 3 0 0 0 0 0 0 0 -1 -1 0 0 0;
0 0 0 0 -1 0 0 0 0 3 0 0 0 0 0 0 0 0 -1 -1 0;
0 0 0 0 0 -1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 -1;% row?10
0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 -0 0 0 0 0 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0;%row 15
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0;
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0;
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0;
0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1;
];% 21-node tree, but root node (node 1) failure
Lshu12=[2 -1 -1 0 0 0 0 0 0 0 0 0;
-1 3 0 -1 -1 0 0 0 0 0 0 0;
-1 0 3 0 0 -1 -1 0 0 0 0 0;
0 -1 0 3 0 0 0 -1 -1 0 0 0;
0 -1 0 0 3 0 0 0 0 -1 -1 0;
0 0 -1 0 0 1 0 0 0 0 0 0;
0 0 -1 0 0 0 2 0 0 0 0 -1;
0 0 0 -1 0 0 0 1 0 0 0 0;
0 0 0 -1 0 0 0 0 1 0 0 0;
0 0 0 0 -1 0 0 0 0 1 0 0;
0 0 0 0 -1 0 0 0 0 0 1 0;
0 0 0 0 0 0 -1 0 0 0 0 1
];%树形12个节点双向结构?
Lcu20= ...
[ 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
-1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;%绗簲琛?
-1 0 0 0 0 2 0 0 0 0 -1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0;%绗崄琛?
0 0 0 0 0 -1 0 0 0 0 2 0 0 0 0 -1 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0;%绗崄浜旇
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1];%绗簩鍗佽
Lhuan20=...
[ 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1;
-1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1;
-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2;
];
% L12: 12 nodes linear network
L12=[1 -1 0 0 0 0 0 0 0 0 0 0;
-1 2 -1 0 0 0 0 0 0 0 0 0;
0 -1 2 -1 0 0 0 0 0 0 0 0;
0 0 -1 2 -1 0 0 0 0 0 0 0;
0 0 0 -1 2 -1 0 0 0 0 0 0;
0 0 0 0 -1 2 -1 0 0 0 0 0;
0 0 0 0 0 -1 2 -1 0 0 0 0;
0 0 0 0 0 0 -1 2 -1 0 0 0;
0 0 0 0 0 0 0 -1 2 -1 0 0;
0 0 0 0 0 0 0 0 -1 2 -1 0;
0 0 0 0 0 0 0 0 0 -1 2 -1;
0 0 0 0 0 0 0 0 0 0 -1 1;
];%单线
% L12c: 12 nodes circular network
L12c=[2 -1 0 0 0 0 0 0 0 0 0 -1;
-1 2 -1 0 0 0 0 0 0 0 0 0;
0 -1 2 -1 0 0 0 0 0 0 0 0;
0 0 -1 2 -1 0 0 0 0 0 0 0;
0 0 0 -1 2 -1 0 0 0 0 0 0;
0 0 0 0 -1 2 -1 0 0 0 0 0;
0 0 0 0 0 -1 2 -1 0 0 0 0;
0 0 0 0 0 0 -1 2 -1 0 0 0;
0 0 0 0 0 0 0 -1 2 -1 0 0;
0 0 0 0 0 0 0 0 -1 2 -1 0;
0 0 0 0 0 0 0 0 0 -1 2 -1;
-1 0 0 0 0 0 0 0 0 0 -1 2;
];%环形
% Lsu12=[2 -1 -1 0 0 0 0 0 0 0 0 0;
% -1 3 0 -1 -1 0 0 0 0 0 0 0;
% -1 0 3 0 0 -1 -1 0 0 0 0 0;
% 0 -1 0 3 0 0 0 -1 -1 0 0 0;
% 0 -1 0 0 3 0 0 0 0 -1 -1 0;
% 0 0 -1 0 0 1 0 0 0 0 0 0;
% 0 0 -1 0 0 0 2 0 0 0 0 -1;
% 0 0 0 -1 0 0 0 1 0 0 0 0;
% 0 0 0 -1 0 0 0 0 1 0 0 0;
% 0 0 0 0 -1 0 0 0 0 1 0 0;
% 0 0 0 0 -1 0 0 0 0 0 1 0;
% 0 0 0 0 0 0 -1 0 0 0 0 1
% ];%树形