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- W2034204728 abstract "We would like to classify the vertices of a hypergraph in the way that ‘similar’ vertices (those having many incident edges in common) belong to the same cluster. The problem is formulated as follows: given a connected hypergraph on n vertices and fixing the integer k(1<k⩽n), we are looking for k-partition of the set of vertices such that the edges of the corresponding cut-set be as few as possible. We introduce some combinatorial measures characterizing this structural property and give upper and lower bounds for them by means of the k smallest eigenvalues of the hypergraph. For this purpose the notion of spectra of hypergraphs — which is the generalization of C-spectra of graphs — is also introduced together with k-dimensional Euclidean representations. We shall that the existence of k 'small' eigenvalues is a necessary but not sufficient condition for the existence of a good clustering. In addition the representatives of the vertices in an optimal k-dimensional Euclidean representation of the hypergraph should be well separated by means of their Euclidean distances. In this case the k-partition giving the optimal clustering is also obtained by this classification method." @default.
- W2034204728 created "2016-06-24" @default.
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- W2034204728 date "1993-07-01" @default.
- W2034204728 modified "2023-09-29" @default.
- W2034204728 title "Spectra, Euclidean representations and clusterings of hypergraphs" @default.
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- W2034204728 doi "https://doi.org/10.1016/0012-365x(93)90322-k" @default.
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