Clustering by hypergraphs and dimensionality of cluster systems by S. Albeverio and S.V. Kozyrev.
Abstract:
In the present paper we discuss the clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss a structure of a hypergraph above this graph. We propose two definitions of dimension for hyperedges of this hypergraph and show that for the multidimensional p-adic case both dimensions are reduced to the number of p-adic parameters.
We discuss the application of the hypergraph clustering procedure to the construction of phylogenetic graphs in biology. In this case the dimension of a hyperedge will describe the number of sources of genetic diversity.
A pleasant reminder that hypergraphs and hyperedges are simplifications of the complexity we find in nature.
If hypergraphs/hyperedges are simplifications, what would you call a graph/edges?
A simplification of a simplification?
Graphs are useful sometimes.
Useful sometimes doesn’t mean useful at all times.