parents (G,v)
The parents of v are the all the vertices u such that u,v is in the directed edge set of the MixedGraph G. So the parents of a vertex v are exactly those vertices of the largest digraph component of a mixed graph that point to v.
i1 : G = mixedGraph(graph{{3,1}},digraph {{1,2},{2,3}},bigraph {{3,4},{2,4}}) o1 = MixedGraph{Bigraph => Bigraph{2 => {4} }} 3 => {4} 4 => {3, 2} Digraph => Digraph{1 => {2}} 2 => {3} 3 => {} Graph => Graph{1 => {3}} 3 => {1} o1 : MixedGraph
i2 : parents (G,1) o2 = set {} o2 : Set
i3 : parents (G,2) o3 = set {1} o3 : Set
i4 : parents (G,3) o4 = set {2} o4 : Set