J = inducedGraph(G,L,OriginalRing=>true)
K = inducedHyperGraph(H,L,OrignalRing=>true)
When OriginalRing is set to true, inducedGraph or inducedHyperGraph returns a (hyper)graph with the original (larger) ring attached rather than the subring only involving the variables of L.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/EdgeIdeals.m2:4346:0.