%0 Journal Article %1 andhofmann2022edgeconnectivity %A Hofmann, Tobias %A Schwerdtfeger, Uwe %D 2022 %J Linear Algebra and its Applications %K crc1410 e01 %P 34-47 %R 10.1016/j.laa.2022.01.012 %T Edge-connectivity matrices and their spectra %V 640 %X The edge-connectivity matrix of a weighted graph is the matrix whose off-diagonal v-w entry is the weight of a minimum edge cut separating vertices vand w. Its computation is a classical topic of combinatorial optimization since at least the seminal work of Gomory and Hu. In this article, we investigate spectral properties of these matrices. In particular, we provide tight bounds on the smallest eigenvalue and the energy. Moreover, we study the eigenvector structure and show in which cases eigenvectors can be easily obtained from matrix entries. These results in turn rely on a new characterization of those nonnegative matrices that can actually occur as edge-connectivity matrices.

@article{andhofmann2022edgeconnectivity, abstract = {The edge-connectivity matrix of a weighted graph is the matrix whose off-diagonal v-w entry is the weight of a minimum edge cut separating vertices vand w. Its computation is a classical topic of combinatorial optimization since at least the seminal work of Gomory and Hu. In this article, we investigate spectral properties of these matrices. In particular, we provide tight bounds on the smallest eigenvalue and the energy. Moreover, we study the eigenvector structure and show in which cases eigenvectors can be easily obtained from matrix entries. These results in turn rely on a new characterization of those nonnegative matrices that can actually occur as edge-connectivity matrices.}, added-at = {2022-05-02T13:37:09.000+0200}, author = {Hofmann, Tobias and Schwerdtfeger, Uwe}, biburl = {https://www.bibsonomy.org/bibtex/2f459b05266f135dfaa76dfa5408f479b/hybridsocieties}, doi = {10.1016/j.laa.2022.01.012}, interhash = {c4fb333a988d406be81bd23923d398e4}, intrahash = {f459b05266f135dfaa76dfa5408f479b}, journal = {Linear Algebra and its Applications}, keywords = {crc1410 e01}, pages = {34-47}, timestamp = {2022-05-05T15:55:34.000+0200}, title = { Edge-connectivity matrices and their spectra}, volume = 640, year = 2022 }