Justin,

I would think that Map might be faster:

s35vertlist = Map[VertexDegree[Subgraph[s35, #]] &, cyclelists35]

Sow works like this -- you don't append to the list -- it just collects the values. I do not recommend this in your case because you want a value returned for every element in your cyclelist

s35vertlist = 
 Reap[Do[Sow[VertexDegree[Subgraph[s35, cyclelists35[[i]]]]], {i, 
    Length[cyclelists35]}]]

Try doing an AbsoluteTiming[] for your loop and the Map and post the times. I am guessing that the Map is faster.

Regards

Sorry, Crossed with Kuda's post at the same time... I would also time Kuda's table approach to see if it is faster than the loop and/or the Map. Curious to know which is faster.

(Also, if you compile the function you will probably get a significant speedup with any of the approaches)