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edited Apr 13, 2017 at 12:55

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This is uncompleted answer for this post this post based on NearestNeighborGraph.I'm lost in how to deal with that source vertices(whose vertex in-degree is 0.) in g,but it has better efficiency than accepted answer accepted answer currently.Maybe somebody can finish it,so I post it still:

SeedRandom[8]
p = RandomReal[10, {400, 2}];
g = NearestNeighborGraph[p, 1, DirectedEdges -> True]

c = Catenate[
   Thread[Rule[List @@ #, EuclideanDistance @@ #/2]] & /@ 
    First /@ FindCycle[g, {2}, All]];
circle = Catenate[
   FixedPointList[
    Function[c, 
     Rule[#, EuclideanDistance[#, 
          t = Last[VertexOutComponent[g, #, 1]]] - (t /. c)] & /@ 
      Complement[VertexInComponent[g, First /@ c, 1], First /@ c]], 
    c]];
Graphics[{Circle @@@ circle}]

As you can see,there are some overlap circles.They are all source vertices.If I don't draw it,it will not be overlap anymore:

Graphics[{Circle @@@ 
   Select[circle, VertexInDegree[g, First[#]] != 0 &]}]

This is uncompleted answer for this post based on NearestNeighborGraph.I'm lost in how to deal with that source vertices(whose vertex in-degree is 0.) in g,but it has better efficiency than accepted answer currently.Maybe somebody can finish it,so I post it still:

SeedRandom[8]
p = RandomReal[10, {400, 2}];
g = NearestNeighborGraph[p, 1, DirectedEdges -> True]

c = Catenate[
   Thread[Rule[List @@ #, EuclideanDistance @@ #/2]] & /@ 
    First /@ FindCycle[g, {2}, All]];
circle = Catenate[
   FixedPointList[
    Function[c, 
     Rule[#, EuclideanDistance[#, 
          t = Last[VertexOutComponent[g, #, 1]]] - (t /. c)] & /@ 
      Complement[VertexInComponent[g, First /@ c, 1], First /@ c]], 
    c]];
Graphics[{Circle @@@ circle}]

As you can see,there are some overlap circles.They are all source vertices.If I don't draw it,it will not be overlap anymore:

Graphics[{Circle @@@ 
   Select[circle, VertexInDegree[g, First[#]] != 0 &]}]

This is uncompleted answer for this post based on NearestNeighborGraph.I'm lost in how to deal with that source vertices(whose vertex in-degree is 0.) in g,but it has better efficiency than accepted answer currently.Maybe somebody can finish it,so I post it still:

SeedRandom[8]
p = RandomReal[10, {400, 2}];
g = NearestNeighborGraph[p, 1, DirectedEdges -> True]

c = Catenate[
   Thread[Rule[List @@ #, EuclideanDistance @@ #/2]] & /@ 
    First /@ FindCycle[g, {2}, All]];
circle = Catenate[
   FixedPointList[
    Function[c, 
     Rule[#, EuclideanDistance[#, 
          t = Last[VertexOutComponent[g, #, 1]]] - (t /. c)] & /@ 
      Complement[VertexInComponent[g, First /@ c, 1], First /@ c]], 
    c]];
Graphics[{Circle @@@ circle}]

As you can see,there are some overlap circles.They are all source vertices.If I don't draw it,it will not be overlap anymore:

Graphics[{Circle @@@ 
   Select[circle, VertexInDegree[g, First[#]] != 0 &]}]

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Improved spelling of title

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edit approved Dec 22, 2016 at 12:34

Andrew Swann

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How to deal with this sourethese source vertices?

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occurred Dec 17, 2016 at 3:51

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occurred Dec 16, 2016 at 17:31

Bounty Started worth 50 reputation by yode

occurred Dec 16, 2016 at 17:31

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edited Dec 12, 2016 at 20:17

yode

27.2k
4
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This is uncompleted answer for this post based on NearestNeighborGraph.I'm lost in how to deal with that source vertexvertices(whose vertex in-degree is 0.) in graphg,but it has better efficiency than accepted answer currently.Maybe somebody can finish it,so I post it still:

SeedRandom[8]
p = RandomReal[10, {400, 2}];
g = NearestNeighborGraph[p, 1, DirectedEdges -> True]

c = Catenate[
   Thread[Rule[List @@ #, EuclideanDistance @@ #/2]] & /@ 
    First /@ FindCycle[g, {2}, All]];
circle = Catenate[
   FixedPointList[
    Function[c, 
     Rule[#, EuclideanDistance[#, 
          t = Last[VertexOutComponent[g, #, 1]]] - (t /. c)] & /@ 
      Complement[VertexInComponent[g, First /@ c, 1], First /@ c]], 
    c]];
Graphics[{Circle @@@ circle}]

As you can see,there are some overlap circlecircles.They are all source vertexvertices.If I don't draw it.It,it will not be no overlap anymore:

Graphics[{Circle @@@ 
   Select[circle, VertexInDegree[g, First[#]] != 0 &]}]

This is uncompleted answer for this post based on NearestNeighborGraph.I'm lost in how to deal with that source vertex(whose vertex in-degree is 0.) in graph,but it has better efficiency.Maybe somebody can finish it,so I post it still:

SeedRandom[8]
p = RandomReal[10, {400, 2}];
g = NearestNeighborGraph[p, 1, DirectedEdges -> True]

c = Catenate[
   Thread[Rule[List @@ #, EuclideanDistance @@ #/2]] & /@ 
    First /@ FindCycle[g, {2}, All]];
circle = Catenate[
   FixedPointList[
    Function[c, 
     Rule[#, EuclideanDistance[#, 
          t = Last[VertexOutComponent[g, #, 1]]] - (t /. c)] & /@ 
      Complement[VertexInComponent[g, First /@ c, 1], First /@ c]], 
    c]];
Graphics[{Circle @@@ circle}]

As you can see,there are some overlap circle.They are all source vertex.If I don't draw it.It will be no overlap anymore:

Graphics[{Circle @@@ 
   Select[circle, VertexInDegree[g, First[#]] != 0 &]}]

This is uncompleted answer for this post based on NearestNeighborGraph.I'm lost in how to deal with that source vertices(whose vertex in-degree is 0.) in g,but it has better efficiency than accepted answer currently.Maybe somebody can finish it,so I post it still:

SeedRandom[8]
p = RandomReal[10, {400, 2}];
g = NearestNeighborGraph[p, 1, DirectedEdges -> True]

c = Catenate[
   Thread[Rule[List @@ #, EuclideanDistance @@ #/2]] & /@ 
    First /@ FindCycle[g, {2}, All]];
circle = Catenate[
   FixedPointList[
    Function[c, 
     Rule[#, EuclideanDistance[#, 
          t = Last[VertexOutComponent[g, #, 1]]] - (t /. c)] & /@ 
      Complement[VertexInComponent[g, First /@ c, 1], First /@ c]], 
    c]];
Graphics[{Circle @@@ circle}]

As you can see,there are some overlap circles.They are all source vertices.If I don't draw it,it will not be overlap anymore:

Graphics[{Circle @@@ 
   Select[circle, VertexInDegree[g, First[#]] != 0 &]}]

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asked Dec 12, 2016 at 19:07

yode

27.2k
4
66
174

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How to deal with this sourethese source vertices?