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I want to extract a couple of nodes from a graph to study its robustness. I would do it manually, eliminating from the list of connections the ones that include the particular node, but the list es very long.

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    $\begingroup$ If you have a Graph, then you could take its VertexList and remove the node you want and then apply Subgraph[g,newVertices]. $\endgroup$ – halirutan May 9 '17 at 3:32
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You can delete nodes using VertexDelete.

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