## Sunday, January 12, 2014

### Weighted hypergraphs

The idea of a weighted hypergraph provides a suitable generalization of weighted graphs, metric spaces, and measure spaces. Predicates are provided for each of these classes of weighted hypergraphs in the system:
(metric-space?
(weighted-hypergraph.
#{0 1 2}
{#{0} 0, #{1} 0, #{2} 0, #{0 1} 1, #{0 2} 1, #{1 2} 1}))

(measure-space?
(weighted-hypergraph.
#{0 1}
{#{} 0, #{0} 1/2, #{1} 1/2}, #{0 1} 1}))

Amongst the measure spaces there is a class of distributions whose weights all range from zero to one inclusive. Amongst the distributions there are special classes of distributions such as uniform distributions and degenerate distributions among others.