HyperG (version 1.0.0)

hypergraph.entropy: Hypergraph Entropy

Description

The hypergraph entropy, which is a sum of the suitably scaled eigenvalues of the hypergraph Laplacian.

Usage

hypergraph.entropy(h)

Arguments

h

a hypergraph.

Value

a number.

Details

Bretto, page 9, defines hypergraph entropy as follows. Let L'(h) be the Laplacian of h divided by the sum of its diagonal. Then the \(|V|-1\) eigenvalues sum to 1, and the entropy is defined by \(-sum(\lambda_i\log_2\lambda_i)\).

References

Bretto, Alain, Hypergraph theory, An introduction. Springer, 2013.

See Also

hypergraph_laplacian_matrix.

Examples

# NOT RUN {
h <- hypergraph_from_edgelist(list(3:4,1:3,c(3,5,7:10),c(4,6),c(3,5,8)))
hypergraph.entropy(h) 
## 2.802822
# }