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HyperBagGraphs (hb-graphs as short) extend hypergraphs by allowing thehyperedges to be multisets. Multisets are composed of elements that have amultiplicity. When this multiplicity has positive integer values, itcorresponds to non ordered lists of potentially duplicated elements. We definehb-graphs as family of multisets over a vertex set; natural hb-graphscorrespond to hb-graphs that have multiplicity function with positive integervalues. Extending the definition of e-adjacency to natural hb-graphs, we definedifferent way of building an e-adjacency tensor, that we compare before havinga final choice of the tensor. This hb-graph e-adjacency tensor is used withhypergraphs.

Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hb-graphs and Related e-adjacency Tensors