I = edgeIdeal H
The edge ideal of a (hyper)graph is a squarefree monomial ideal in which the minimal generators correspond to the edges of a (hyper)graph. Along with coverIdeal, the function edgeIdeal enables us to translate many graph theoretic properties into algebraic properties.
When the input is a finite simple graph, that is, a graph with no loops or multiple edges, then the edge ideal is a quadratic squarefree monomial ideal generated by terms of the form $x_ix_j$ whenever $\{x_i,x_j\}$ is an edge of the graph.






When the input is a hypergraph, the edge ideal is a squarefree monomial ideal generated by monomials of the form $x_{i_1}x_{i_2}...x_{i_s}$ whenever $\{x_{i_1},...,x_{i_s}\}$ is an edge of the hypergraph. Because all of our hypergraphs are clutters, that is, no edge is allowed to be a subset of another edge, we have a bijection between the minimal generators of the edge ideal of hypergraph and the edges of the hypergraph.



The object edgeIdeal is a method function.