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Published in:
01-11-2021 | COMPUTER METHODS
Signatures of Extremal 2-Unifrom Hypergraphs
Published in: Journal of Computer and Systems Sciences International | Issue 6/2021
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Abstract
Storing hypergraphs in computer memory is rather inefficient, since the main storage method is an incidence matrix or a list of hyper edges. For n-vertex k-uniform hypergraphs (UHs), it is possible to specify an adjacency matrix but its volume is nk. For extremal UHs, it becomes possible to use the base in the form of a storage object; it takes up less space in memory than a list of hyper edges, but it is not always convenient from a practical point of view. Here we consider a new concept: the signature of an extremal 2-UH, which is a nonnegative integer and uniquely characterizes the hypergraph. For this representation, algorithms are described for constructing an extremal 2-UH in the form of an adjacency matrix or base from a signature. Algorithms for obtaining a signature from an arbitrary adjacency matrix or base of an extremal 2-UH are also presented.