Find all reachable nodes in a graph

Mathematica 63 40 37

My earlier submission was incorrect. I had misinterpreted what ConnectedComponents returns. The present approach relies on Belisarius' suggestion to useVertexOutComponent. 3 additional chars saved by alephalpha.

The following generates an 11 by 11 adjacency matrix of 0's and 1's, where 1 indicates that the vertex with the row number is connected directly to the vertex corresponding to column number of the cell. (SeedRandom ensures that your matrix a will match mine.)

SeedRandom[21]
a = Array[RandomChoice[{0.9, 0.1} -> {0, 1}] &, {11, 11}];

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Example

(37 chars)

 AdjacencyGraph@a~VertexOutComponent~4

{4, 1, 7, 8, 9, 3}

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Verifying

The directed graph displays how to reach vertices {1, 7, 8, 9, 3} from vertex 4.

AdjacencyGraph[a, ImagePadding -> 30, VertexLabels -> "Name"]

Python 2.7 - 80 65

def R(G,s):
 k=a={s}
 while k:a=a|k;k|=set(G[k.pop()])-a
 print a

GolfScript, 27 24 characters

{:G,{G{1$&},{)||}/}*}:C;

This code implements the operator C which takes starting node and graph on the stack and leaves a list of reachable notes on the stack after execution.

Example (online):

[1] [[1 [2 3]][2 [3]][3 [1]][4 [2]]] C
# returns [1 2 3]