Skip to main content

functions - Vertex descendants subgraph


Keywords: vertex, ancestors, descendants, subgraph, directed graph, flow subtree





So let's say we have a TreeGraph:


opts = Sequence[
EdgeShapeFunction -> GraphElementData["FilledArrow", "ArrowSize" -> 0.02],
VertexLabels -> "Name"
];

data = RandomInteger[#] -> # + 1 & /@ Range[0, 10];

g = TreeGraph[data, opts]


enter image description here


Question


What's the proper/functional way to get subgraph containing only successors of given node with respect to the flow.


I'm not very familiar with graphs so I have a solution (bottom) but I suppose I'm missing some basic graph related functions.


Example


for 0 it would be the whole graph


for 4 it would be {4->5, 5->8, 8->9}


Problem


I can't find appriopriate function and AdjacencyList/IncidenceList don't respect the direction of the flow:


topV = 4;

HighlightGraph[g,
{Style[topV, Blue], AdjacencyList[g, topV, 2], IncidenceList[g, topV, 2]}
]

enter image description here


My brute force but not so stupid solution:


let's cut the inflow! so the AdjacencyList won't leave this way :)


subTreeWF[g, 4] // TreeGraph[#, opts] &

enter image description here



I'm assuming here that the topNode is not the final one, in such case additional check is needed.


subTreeWF[treeGraph_, topNode_] := Module[{edges},
edges = EdgeList @ treeGraph;
edges = DeleteCases[ edges,
(Rule | DirectedEdge | UndirectedEdge)[_, topNode]
];

IncidenceList[Graph @ edges, topNode, \[Infinity]]

]




g = Graph[RandomInteger[#] -> # + 1 & /@ Range[0, 30], opts];

topV = 5;

HighlightGraph[g, {Style[topV, Blue], subTreeWF[g, topV]}]

enter image description here



Answer




You are looking for VertexOutComponent.


VertexOutComponent[g, 4]

gives you the successors of 4. Use Subgraph to get an actual graph out of those. With HighlightGraph, you can also use a subgraph, it will highlight both vertices and edges: HighlightGraph[g, Subgraph[g, VertexOutComponent[g, 4]]].


For visualizing the graph, use GraphLayout -> "LayeredDigraphEmbedding", which will place the root at the topmost position. Some other tree layouts have a "RootVertex" suboptions to achieve this (e.g. for undirected where anything can be the "root").


Comments

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...