Graphs and Hypergraphs

By C. Berge. Clustering, 2021

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How researchers see this paper

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Networks beyond pairwise interactions: structure and dynamics (2020, background): “For example, in the case of hypergraphs, n is the total number of nodes while m is the number of hyperedges [18, 82].”
Minimum vertex degree condition for tight Hamiltonian cycles in 3‐uniform hypergraphs (2016, background): “An early notion of cycles in hypergraphs appeared in the work of Berge [1] (see also [2]) more than 40 years ago.”
Hypergraph Convolution and Hypergraph Attention (2019, background): “GCN [22] and Diusion CNN [25] as its special cases. As analyzed above, most existing variants of GNN assume pairwise relationships between objects, while our work operates on a high-order hypergraph [43,44] where the between-object relationships are beyond pairwise. Hypergraph learning methods dier ”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “end" [22,50,76]. Accordingly, researchers have started to investigate richer mathematical modeling frameworks in the past years, such as simplicial complexes [39,49], set systems and hypergraphs [10,15], and aliation graphs [31], which all account for non-dyadic and higher-order interactions. S”