"There are several notions which fall under the name “hypergraph”, and we do not follow conventions too closely here. For us, a hypergraph is simply a kind of graph which has different types of nodes and edges, with edges allowed to be possibly “open” in the sense that they are attached only on one end to some node. Composition of such graphs to build new graphs is possible by connecting open edges together (though we only allow edges of the same type to connect). The following picture illustrates such a composition, with different types of edges indicated by different types of lines."