Weighted subdirect sum of Nekrasov matrices

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Abstract
The weighted subdirect sum of matrices plays a fundamental role in applications involving overlapping structures, such as multilayer network analysis and overlapping block iterative methods for solving linear systems. In this paper, some sufficient conditions are presented to ensure that the weighted subdirect sum of Nekrasov matrices is in the class of Nekrasov matrices. We obtain, in particular, that the weighted $1$-subdirect sum of a Nekrasov matrix and a strictly diagonally dominant matrix remains a Nekrasov matrix. Theoretical results are complemented by numerical examples demonstrating the validity and applicability of the proposed conditions.

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