On Spectral Properties of Signed Laplacians With Connections to Eventual Positivity
On Spectral Properties of Signed Laplacians With Connections to Eventual Positivity
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DOI：
10.1109/tac.2020.3008300
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发表时间：
2020-09
影响因子：
6.8
通讯作者：
Wei Chen;Dan Wang;Ji Liu;Yongxin Chen;Sei Zhen Khong;T. Başar;K. Johansson;L. Qiu
中科院分区：
文献类型：
--
作者：
Wei Chen;Dan Wang;Ji Liu;Yongxin Chen;Sei Zhen Khong;T. Başar;K. Johansson;L. Qiu
签名图已出现在各种应用中，从社交网络到生物网络，从分布式控制和计算到电力系统。在本文中，我们研究了未指向签名的图形的签名laplacians的光谱特性。我们发现，通过KRON还原和多层网络理论，签名的Laplacian在负权重的情况下是正能量的。对于不确定的签名的拉普拉斯人，我们用相同的框架来表征他们的惯性。此外，我们在签名的Laplacians，广义$ M $ am-Matrices和最终呈指数为正的矩阵之间建立联系。
Signed graphs have appeared in a broad variety of applications, ranging from social networks to biological networks, from distributed control and computation to power systems. In this article, we investigate spectral properties of signed Laplacians for undirected signed graphs. We find conditions on the negative weights under which a signed Laplacian is positive semidefinite via the Kron reduction and multiport network theory. For signed Laplacians that are indefinite, we characterize their inertias with the same framework. Furthermore, we build connections between signed Laplacians, generalized $M$-matrices, and eventually exponentially positive matrices.