Textiles have an important role in many cultures and have been digitised. They are three-dimensional objects and have complex structures, especially archaeological fabric specimens and artifact textiles created manually by traditional craftsmen. In this article, we propose a novel algorithm for textile classification based on their structures. First, a hypergraph is used to represent the textile structure. Second, multisets of
k
-neighbourhoods are extracted from the hypergraph and converted to one feature vector for representation of each textile. Then, the
k
-neighbourhood vectors are classified using seven most popular supervised learning methods. Finally, we evaluate experimentally the different variants of our approach on a data set of 1,600 textile samples with the 4-fold cross-validation technique. The experimental results indicate that comparing the variants, the best classification accuracies are 0.999 with LR, 0.994 with LDA, 0.996 with KNN, 0.994 with CART, 0.998 with NB, 0.974 with SVM, and 0.999 with NNM.