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

2025/08/04 by van der Hofstad, Remco, Müller, Noela, Zhu, Haodong · 1 citation
#05C80 #60B20 #94B05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.02813

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 \citejanson2009new, which enables the application of combinatorial techniques from \citecoja2022rank, HofMul25.

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