Geodesic
Eigenvalue pairing in the response matrix for a class of network models with circular symmetry
Miriam Farber1 ; Charles R Johnson2 ; Wei Zhen3
1Department of Mathematics, Technion - Israel Institute of Technology
2Department of Mathematics, Collage of William and Mary
3Department of Mathematics, Imperial College
The electronic journal of combinatorics, Tome 20 (2013) no. 3
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We consider the response matrices in certain weighted networks that display a circular symmetry. It had been observed empirically that these exhibit several paired (multiplicity two) eigenvalues. Here, this pairing is explained analytically for a version of the model more general than the original. The exact number of necessarily paired eigenvalues is given in terms of the structure of the model, and the special structure of the eigenvectors is also described. Examples are provided.
DOI : 10.37236/3318
Classification : 05C50, 15A18, 90B10, 05C10
Mots-clés : circular planar graph, Dirichlet-to-Neumann matrix, eigenvalue pairing, resistor network

Miriam Farber  1   ; Charles R Johnson  2   ; Wei Zhen  3

1 Department of Mathematics, Technion - Israel Institute of Technology
2 Department of Mathematics, Collage of William and Mary
3 Department of Mathematics, Imperial College 
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Miriam Farber; Charles R Johnson; Wei Zhen. Eigenvalue pairing in the response matrix for a class of network models with circular symmetry. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/3318

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