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arXiv · 2508.02813

The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields

Remco van der Hofstad·Noela Müller·Haodong Zhu
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Abstract

We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the (multi-)graph. Our main result demonstrates that the asymptotic behavior of the normalized rank of the adjacency matrix neither depends on the fixed edge-weights, nor on which field they are chosen from. Our approach relies on a novel adaptation of the component exploration method of \cite{janson2009new}, which enables the application of combinatorial techniques from \cite{coja2022rank, HofMul25}.

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Remco van der Hofstad, Noela Müller, Haodong Zhu. 2025-08-04. The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields. https://arxiv.org/abs/2508.02813

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