TY - GEN
T1 - Characterizing the positive semidefiniteness of signed Laplacians via Effective Resistances
AU - Chen, Wei
AU - Liu, Ji
AU - Chen, Yongxin
AU - Khong, Sei Zhen
AU - Wang, Dan
AU - Başar, Tamer
AU - Qiu, Li
AU - Johansson, Karl H.
PY - 2016/12/27
Y1 - 2016/12/27
N2 - A symmetric signed Laplacian matrix uniquely defines a resistive electrical circuit, where the negative weights correspond to negative resistances. The positive semidefiniteness of signed Laplacian matrices is studied in this paper using the concept of effective resistance. We show that a signed Laplacian matrix is positive semidefinite with a simple zero eigenvalue if, and only if, the underlying graph is connected, and a suitably defined effective resistance matrix is positive definite.
AB - A symmetric signed Laplacian matrix uniquely defines a resistive electrical circuit, where the negative weights correspond to negative resistances. The positive semidefiniteness of signed Laplacian matrices is studied in this paper using the concept of effective resistance. We show that a signed Laplacian matrix is positive semidefinite with a simple zero eigenvalue if, and only if, the underlying graph is connected, and a suitably defined effective resistance matrix is positive definite.
UR - http://www.scopus.com/inward/record.url?scp=85010749037&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85010749037&partnerID=8YFLogxK
U2 - 10.1109/CDC.2016.7798396
DO - 10.1109/CDC.2016.7798396
M3 - Conference contribution
AN - SCOPUS:85010749037
T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
SP - 985
EP - 990
BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th IEEE Conference on Decision and Control, CDC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -