On eigenvector structure of weakly balanced networks

Ranveer Singh

Physica A: Statistical Mechanics and its Applications, 2019, vol. 527, issue C

Abstract: A signed network is called weakly balanced when its vertex set can be partitioned into two or more vertex subsets (clusters) such that every positive edge joins the vertices of the same subset and every negative edge joins the vertices of different subsets. Finding a spectral criterion for weakly balanced networks is an open problem. In this paper, the eigenvector structure of some weakly balanced signed networks is calculated. The eigenvector structure helps in the transformation of (−1,0,1)-adjacency matrices of these networks to tridiagonal matrices. Hence, we provide partial results on eigenvalues of these networks, and in general, their spectra can be calculated using the existing numerical methods.

Keywords: Signed network; Eigenvalues; Weakly balanced networks (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119306697

DOI: 10.1016/j.physa.2019.121093

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