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I am not sure if this is the right list, but here's my question and it comes from studying social science network data:

I have a graph (G) and a real valued function (F) on the vertices (V). Is there a way to study the "surface" defined by (v, f(v)) in GxR?  In other words, how do I translate the ides of multivariable calculus and differential geometry into the discrete world?

A google search does show that that there is a literature (e.g., there is the discrete Laplacian), but it mainly applies to mesh grids (ie, you chop up the domain of the function into a grid), but not for an arbitrary graph, which is my issue. Any tips? What would I need to know about calculus on graphs that might be different than the continuous version?

Fabio

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