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  • $\begingroup$ Seems like removing the unwanted edges form the definition is the most straightforward way: in this case, Graph[Most[e]] will give you the same connectivity as what you are asking for. (The picture doesn't look the same, but the graph is the same). $\endgroup$ Commented May 31, 2013 at 20:04
  • $\begingroup$ If your graph g is already defined, then you can use EdgeList[g] to get the edges, then remove the ones you want. $\endgroup$ Commented May 31, 2013 at 20:35
  • $\begingroup$ Your question answers perfectly my original question. Would you happen to know how I can preserve the EdgeStyle associated with the edges? Seems like Options[g,{EdgeStyle}] doesn't work because it includes an EdgeStyle for every edge in the original graph g. Anyway, since I changed the meanings of my question after you had answered, I will definitely accept your answer. I will keep working on the problem and update your question if I crack it. $\endgroup$ Commented May 31, 2013 at 20:51
  • $\begingroup$ I'm not sure how to do it staying within EdgeStyle. A more straightforward way would be to define the styling via a list and to then index into that list exactly as you are indexing into the edgelist. That way the styling would stay consistent. $\endgroup$ Commented May 31, 2013 at 21:09
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    $\begingroup$ If you want to preserve the layout of the graph, check out this answer about keep node locations mathematica.stackexchange.com/a/11106/2393 $\endgroup$ Commented Jun 1, 2013 at 5:58