Mathematica, 29 chars
{s}//.l_List:>(l⋃##&@@(l/.G))
Example:
G = {1 -> {2, 3}, 2 -> {3}, 3 -> {1}, 4 -> {2}}; s = 1;
{s}//.l_List:>(l⋃##&@@(l/.G))
{1, 2, 3}
alephalpha
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