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.
