Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a large graph $G$, which may be either directed or undirected. How would I use DepthFirstScan[] or BreadthFirstScan[] to efficiently and uniformly sample the set of vertices a fixed shortest distance of $D$ away from some vertex $v_i \in V$?

share|improve this question
up vote 2 down vote accepted

Start with a graph and a distance d:

g = RandomGraph[BarabasiAlbertGraphDistribution[1000, 1]];

d = 5

Find the distance of a vertex (e.g. vertex 300) to all others:

distances = GraphDistance[g, 300];

Sample k vertices from those with distance d from 300:

 Pick[VertexList[g], distances, d],
share|improve this answer
other variance could be: Reap[CheckAbort[ BreadthFirstScan[g, 300, "DiscoverVertex" -> ((If[#3 > 5, Abort[]]; If[#3 == d, Sow[#1]]) &)], "Done"]][[2, 1]] or Complement[AdjacencyList[g, 300, d], AdjacencyList[g, 300, d - 1]] – halmir Apr 24 '13 at 14:13
@halmir Why don't you post it as another answer? Instead of Abort[] I'd use Return[] (after wrapping the whole thing in a function). Or use two-argument Return. It's cleaner. – Szabolcs Apr 24 '13 at 15:08
thanks! I will post it. – halmir Apr 24 '13 at 15:20

Alternative way to extract vertices:

g = RandomGraph[BarabasiAlbertGraphDistribution[1000, 1]];
d = 5;
  1. Szabolcs suggestion

    distances = GraphDistance[g, 300];
    set1 = Pick[VertexList[g], distances, d];
  2. using BreadthFirstScan

    set2 = Reap[
      BreadthFirstScan[g, 300, "DiscoverVertex" -> ((If[#3 > 5, Abort[]]; 
      If[#3 == d, Sow[#1]]) &)], "Done"]][[2, 1]];

    with Return[]

    set3 = Reap[
     BreadthFirstScan[g, 300, "DiscoverVertex" -> ((If[#3 > 5, Return[]]; 
     If[#3 == d, Sow[#1]]) &)]][[2, 1]];
  3. using AdjacencyList:

    set4 = Complement[AdjacencyList[g, 300, d], AdjacencyList[g, 300, d - 1]];

Compare results:

In[271]:= Sort[set1] == Sort[set2] == Sort[set3] == Sort[set4]
Out[271]= True
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.