I am taking the time to learn how to analyze networks and want to test if there are differences between two networks over time. Since I am new to R and networks in general, I am hoping to get some help how to compare and analyze network graphs.
Simply, my dataset will contain information on flows between two geographic units (think Census migration data). I want to test if the flows, generally, are different with time. Since I am just starting out, I am not even sure if I am phrasing my question correctly.
I have created a few basic graphs and generated some very basic "summary statistics" on a graph in isolation in R before, so I understand how to get up and running, but I am not really sure where to go from here.
Best Answer
I agree with Srikant, you need to model your process. You mentioned that you had already created some networks in R, what model did you assume?
The way I would tackle this problem, is to form a mathematical model, say an ODE model. For example,
\begin{equation} \frac{dX_i(t)}{dt} = \lambda X_{i-1}(t) -\mu X_{i+1}(t) \end{equation}
where $X_i$ depends on the population at geographic unit $i$. Since you are interested in differences in time, your parameters $\lambda$ may also depend on $t$.
You can fit both models simultaneously and determine if the rates are different.
You problem isn't easy and I don't think there's an simple solution to it.