I am analyzing data relating to networks that evolve over times (more precisely, a snap shot of the network at every discrete time step). Each node of the network denotes a person who perform some action at each time step.
As the network evolves, communities may emerge and we run some detection algorithm to identify these communities at each time step. As part of our analysis, we want to focus on these communities and the nodes within each.
A difficulty here is that these communities are changing (e.g. the number of communities may be different at each step, so are the memberships of these communities), so there is no way to fix the number of columns/variables needed to account for all possible number of communities (and their various structural properties) emerged at each time step. In step 1, there might be just one community, while in step 6 there might be three.
I would like to be able to analyze these data on two levels:
For the detected communities, analyze their network structural properties and see whether they stabilize over time (which would imply that the number of detected communities stabilize too).
For each node of the network, analyze how their actions (and other characteristics) relate to the communities to which they belong to.
If possible, I would like to utilize Stata for such analysis but other tools are OK too. More generally, I am interested in how I should tackle such scenario of analysis properly.