
On Adjacency and eAdjacency in General Hypergraphs: Towards a New eAdjacency Tensor
In graphs, the concept of adjacency is clearly defined: it is a pairwise...
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Adjacency Matrix and Cooccurrence Tensor of General Hypergraphs: Two Well Separated Notions
Adjacency and cooccurrence are two well separated notions: even if they...
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Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hbgraphs and Related eadjacency Tensors
HyperBagGraphs (hbgraphs as short) extend hypergraphs by allowing the h...
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Information Limits for Detecting a Subhypergraph
We consider the problem of recovering a subhypergraph based on an observ...
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Multilayered planar firefighting
Consider a model of fire spreading through a graph; initially some verti...
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CAD Adjacency Computation Using Validated Numerics
We present an algorithm for computation of cell adjacencies for wellbas...
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Node and Edge Eigenvector Centrality for Hypergraphs
Network scientists have shown that there is great value in studying pair...
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On Adjacency and eadjacency in General Hypergraphs: Towards an eadjacency Tensor
Adjacency between two vertices in graphs or hypergraphs is a pairwise relationship. It is redefined in this article as 2adjacency. In general hypergraphs, hyperedges hold for nadic relationship. To keep the nadic relationship the concepts of kadjacency and eadjacency are defined. In graphs 2adjacency and eadjacency concepts match, just as kadjacency and eadjacency do for kuniform hypergraphs. For general hypergraphs these concepts are different. This paper also contributes in a uniformization process of a general hypergraph to allow the definition of an eadjacency tensor, viewed as a hypermatrix, reflecting the general hypergraph structure. This symmetric eadjacency hypermatrix allows to capture not only the degree of the vertices and the cardinality of the hyperedges but also makes a full separation of the different layers of a hypergraph.
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