Recognizing Distance-Count Matrices is Difficult
Paolo Boldi; Flavio Furia; Chiara Prezioso; Ian Stewart · 2025 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
The study found no significant effect — useful as a negative control or null benchmark for your own design.
Abstract (excerpt)
Axiomatization of centrality measures often involves proving that something cannot hold by providing a counterexample (i.e., a graph for which that specific centrality index fails to have a given property). In the context of geometric centralities, building such counterexamples requires constructing a graph with specific distance counts between nodes, as expressed by its distance-count matrix. We prove that deciding whether a matrix is the distance-count matrix of a graph is strongly NP-complete. This negative result implies that a brute-force approach to building this kind of counterexample i
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Metadata source: arXiv