Package: hypergraphs 0.7.5

hypergraphs: Higher-Order Network Analysis

Build and analyze higher-order networks, in which a relation can involve more than two nodes or can depend on more than the current node. Covers the three structure families of the higher-order network literature Battiston et al. (2020) <doi:10.1016/j.physrep.2020.05.004>, plus a text family that reads a corpus as a hypergraph. Every object is read through one accessor, and every sequence-taking verb reads long, wide, list or model input. Memory networks from categorical sequences: higher-order networks with rule extraction Xu, Wickramarathne, and Chawla (2016) <doi:10.1126/sciadv.1600028>, higher-order network embedding Saebi et al. (2020) <doi:10.1089/big.2019.0169>, hypergeometric path anomaly detection LaRock et al. (2020) <doi:10.1137/1.9781611976236.52>, the multi-order generative model Scholtes (2017) <doi:10.1145/3097983.3098145>, higher-order centralities Scholtes, Wider, and Garas (2016) <doi:10.1140/epjb/e2016-60663-0>, a permutation-based Markov order test, a path-dependence diagnostic, and bootstrap and permutation inference for extracted rules. Simplicial complexes: clique, Vietoris-Rips and pathway complexes, Betti numbers, persistent homology, persistence landscapes, bottleneck and Wasserstein distances, and q-analysis. Hypergraphs: construction from network cliques, sliding windows over sequences, bipartite group membership, or embedding nearest neighbours; structural measures; tensor eigenvector centralities Benson (2019) <doi:10.1137/18M1203031>; PageRank with edge-dependent vertex weights Chitra and Raphael (2019) <doi:10.48550/arXiv.1905.08287>; the weighted normalized hypergraph Laplacian of Zhou, Huang, and Scholkopf (2006) <doi:10.7551/mitpress/7503.003.0205> with spectral, symmetric non-negative matrix factorization (NMF), and joint-NMF clustering Hayashi et al. (2020) <doi:10.1145/3340531.3412034> and transductive label spreading; projections to weighted graphs and s-line graphs; Bernoulli-incidence, stochastic-block, uniform and regular random generators; temporal snapshots; hyperedge betweenness and closeness; Infomap ensembles with adjusted- mutual-information medoid selection; Y/T/O motif profiles and null models by degree-preserving swaps and the configuration model; and hypergraph neural networks in native 'torch': the hypergraph neural network (HGNN), hypergraph attention networks (HyperGAT and its heterogeneous variant), the hypergraph convolutional network (HyperGCN), hypergraph networks with hyperedge neurons (HNHN), AllDeepSets and AllSetTransformer. Text hypergraphs: a corpus becomes a weighted document-word hypergraph in either orientation (bag of words with smoothed term frequency-inverse document frequency (tf-idf), token windows, or embedding nearest neighbours), analysed with tidy verbs for clustering, keyword extraction, few-label classification, and null testing.

Authors:Mohammed Saqr [aut, cre, cph]