The most well-known practitioners of this sort of 'topological' approach are Ayasdi, they have some slick demos [1]. The general name for this idea is topological data analysis [2].

I replicated this particular experiment in WL, of course, because it's a 5-minute thing to do [3], and I could actually do the community detection the author alluded to.

But I noticed that the correlation matrix itself is much more suggestive than the graph ends up being, with or without community detection. Take a look at the correlation matrix (note that MatrixPlot does some clever combination of rank and absolute value to get high dynamic range):

http://imgur.com/WKn029o

The tri-diagonal structure is because the original dataset is derived from the pixel counts from successive 4x4 tiles on NIST written-digit images [4].

Those 8x8 matrix of tiles is flattened onto the 64 random variables, so the large correlation with tiles on the left and right explain the 1-off-diagonal orange lines, the other two diagonals are offset by 8 and correspond the high correlation with the tiles above and below. That's the 'connectivity kernel' of a 2D manifold, so to speak.

The curious squiggles in all the other blocks of this matrix are unusual. I don't know what's going on there. Maybe something interesting.

[1] http://www.ayasdi.com/

[2] http://en.wikipedia.org/wiki/Topological_data_analysis

[3] https://www.wolframcloud.com/objects/c7927909-448d-4502-9c1a...

[4] https://archive.ics.uci.edu/ml/machine-learning-databases/op...