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Link to M.SE version:

• http://mathematica.stackexchange.com/questions/130525/how-can-i-remove-a-fraction-p-of-nodes-or-edges-from-a-graph-randomly

Response on the linked post:

To randomly remove a fraction $p$ of vertices or edges from a graph g, you can do the following:

p = 0.1; (* make sure p has a value *)

verticesToRemove = RandomSample[VertexList[g], Round[p VertexCount[g]]]

result = VertexDelete[g, verticesToRemove]

For edges:

edgesToRemove = RandomSample[EdgeList[g], Round[p EdgeCount[g]]]

result = EdgeDelete[g, edgesToRemove]

Is the result still connected? Check it with ConnectedGraphQ.

If the result graph is not connected, you can look at what is the size of the largest component in the result, relative to the total graph size:

Length@First@ConnectedComponents[result]/VertexCount[result]

Try it on a scale free network created using preferential attachment:

g = RandomGraph[BarabasiAlbertGraphDistribution[300, 2]]

Repeat the calculation 100 times and compute the average fraction of the largest component:

Table[
 verticesToRemove = RandomSample[VertexList[g], Round[p VertexCount[g]]];
 result = VertexDelete[g, verticesToRemove];
 Length@First@ConnectedComponents[result]/VertexCount[result],
 {100}
]

N@Mean[%]