The children of v are the all the vertices u such that v,u is in the directed edge set of the MixedGraph G. So the children of a vertex v are exactly those vertices of the largest digraph component of a mixed graph that v points to.
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
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i2 : children (G,1)
o2 = set {2}
o2 : Set
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i3 : children (G,2)
o3 = set {3}
o3 : Set
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i4 : children (G,3)
o4 = set {}
o4 : Set
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