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Is there a way to conditionally take control the flow during a depth-first scan against a TreeGraph?

I have a tree graph whose nodes are constructed as object, and there's a method isTrue[para_] for each node.

isValid[desc] = "Check whether input is valid";
isValid[isTrue, para_] := Module[{result},
    result = SyntaxQ[para];

isNumber[desc] = "Check whether input is a number";
isNumber[isTrue, para_] := Module[{result},
    result = NumberQ[ToExpression[para]];

isInteger[desc] = "Check whether input is an integer";
isInteger[isTrue, para_] := Module[{result},
    result = IntegerQ[ToExpression[para]];

isFraction[desc] = "Check whether input is a fraction";
isFraction[isTrue, para_] := Module[{result},
    result = !IntegerQ[ToExpression[para]];

tree = 
  TreeGraph[{isValid, isNumber, isInteger, isFraction}, 
    {isValid -> isNumber, isNumber -> isInteger, isNumber -> isFraction},

Here is the tree image of the code, The root is isValid.

The structure of tree

If my input is "3.5", I expect the depth-scan flow should be isValid -> isNumber -> isFraction because the isInteger gives False.

I tried Abort[] like (as well as Return[]):

DepthFirstScan[tree, isValid, 
 "DiscoverVertex" -> (If[#[isTrue, "3.5"], Print[#], Abort[]]&)];

But this broke the whole scan flow. What I want is: when the node gives False, it and its child-nodes should be skipped, but the scan should continue scanning the remaining nodes.

share|improve this question
Some advice on coding. isValid can be reduced to isValid[isTrue, para_] := SyntaxQ[para]. Similar reductions can be made to your other functions. – m_goldberg Nov 4 '13 at 12:45
@m_goldberg thanks for your advice. – Michael Nov 4 '13 at 13:11
up vote 3 down vote accepted

DepthFirstScan as well as BreadthFirstScan has no such functionality. However, you can construct a temporary graph without unwanted edges

n = 8;
g = GridGraph[{n, n}, DirectedEdges -> True, 
  VertexStyle -> Thread[Range[n^2] -> RandomChoice[{3, 1} -> {White, Black}, n^2]]]

enter image description here

Here invalid vertices marked by black. Let's delete all corresponding edges

g2 = EdgeDelete[g, DirectedEdge[_, n_] /; PropertyValue[{g, n}, VertexStyle] == Black];

visited = Reap[DepthFirstScan[g2, 1, {"DiscoverVertex" -> (Sow[#] &)}]][[2, 1]];

HighlightGraph[g, visited]

enter image description here

share|improve this answer
thanks a lot. You pointed me a correct way to do this. – Michael Nov 5 '13 at 6:37

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