Very interesting, Marco! The Wiki data can actually be used to reflect on what candidates people view as related. Again your data:

fullnames = {{"Donald", "TRUMP"}, {"Jeb", "BUSH"}, {"Scott", "WALKER"}, {"Marco", "RUBIO"}, 
                     {"Chris", "CHRISTIE"}, {"Ben", "CARSON"}, {"Rand", "PAUL"}, {"Ted", "CRUZ"}, 
                     {"Mike", "HUCKABEE"}, {"John", "KASICH"}, {"Carly", "FIORINA"}};

data = ParallelMap[WolframAlpha[#[[1]] <> " " <> #[[2]], 
{{"PopularityPod:WikipediaStatsData", 1}, "ComputableData"}] &, fullnames];

But I'll get the last year to be fair to the recent campaign and use log plot to see better the details:

recent = TimeSeriesWindow[#, {{2014, 1, 1}, Now}] &@ TemporalData[data];
DateListLogPlot[recent, PlotRange -> All, PlotTheme -> "Detailed", AspectRatio -> 1/4, 
 ImageSize -> 800, PlotLegends -> fullnames[[All, 2]]]

Let's get mutual correlation matrix - note the diagonal INfinity trick - for the self-edge removal in WeightedAdjacencyGraph.

m = Outer[Correlation, #, #, 1] &@ 
QuantityMagnitude[Normal[recent][[All, All, 2]]] (1 - IdentityMatrix[Length[fullnames]]) /. 0. -> Infinity;

Significant negative correlations are hard to get in such data, but positive values can be quite high:

m // Flatten // Sort

MatrixPlot[m, FrameTicks -> {Transpose[{Range[11], #}], Transpose[{Range[11], Rotate[#, Pi/2] & /@ #}]}, 
   ColorFunction -> "Rainbow"] &@fullnames[[All, 2]]

So we are getting a complete weighted graph:

g = WeightedAdjacencyGraph[m, VertexLabels -> Thread[Range[11] -> fullnames[[All, 2]]], 
   VertexSize -> "ClosenessCentrality", VertexStyle -> Opacity[.5]];

FindGraphCommunities still react on EdgeWeight:

comm = FindGraphCommunities[g]

{{1, 5, 6, 9, 10, 11}, {2, 3, 4, 7, 8}}

So I wonder if anyone with actual knowledge of politics can see in this clustering some truth:

CommunityGraphPlot[g, comm]

Right, we should fix that. In the meantime, it's kind of interesting to look more closely at the words I threw out of the earlier clouds, and the context in which they appear. For example, "we need" is such a common phrase in these debates, but what is it that each candidate thinks "we" need?

This is just so much fun and informative; a timely use of current analytics.

connecting them by the times their daily hits overlap

Sort of, yes, but "overlap" is a too broad term. The measure of that is "Correlation" - and it is exactly the name of the function used in the main block of code:

m = Outer[Correlation, #, #, 1] &@ 
QuantityMagnitude[Normal[recent][[All, All, 2]]] (1 - IdentityMatrix[Length[fullnames]]) 
/. 0. -> Infinity;

Communities just group those candidates whose pages viewed by public more synchronously. Wiki data are in hits per day based on weekly averages of daily hits to English-language page. That explanation can be seen on any W|A page under the wiki-data plot - for example: Donald Trump

What if instead of showing what the candidates said, we show what people heard? I wonder if there's a way to pull Twitter data by #demdebate or #gopdebate for a word cloud of reactions?

Very interesting that “people” is prominent in 4/5 of the Democratic word clouds in this this post

http://blog.wolfram.com/2015/10/14/democratic-presidential-debate-word-clouds/

and none of the Republican ones in this post

http://blog.wolfram.com/2015/08/13/the-winner-of-the-gop-presidential-debate/