Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this task. The introduced approach supports various linkage-based clustering algorithms, vertex proximity matrices, and graph representation learning models. We compare over a hundred module combinations on the Stochastic Block Model graphs and real-life datasets. We observe that our best pipelines (Wasserman-Faust and the mutual information-based PPMI proximity, as well as the deep learning-based DNGR representations) perform competitively to the state-of-the-art Leiden and Louvain algorithms. At the same time, unlike the latter, they remain hierarchical. Thus, they output a series of nested partitions of all possible cardinalities which are compatible with each other. This feature is crucial when the number of correct partitions is unknown in advance.