Complex networks (CN) are one of the most important type of graphs in recent years. Publications of Watts-Strogatz (Small World property, 1998) and Barabasi-Albert (Scale Free property, 1999) have started intensive research in this area. CN have been the most often considered in static way. What's about dynamics (evolution) of CN?
One of the possible approach to this problem is making some snapshots on CN, taking their characteristics at some moments and using statistical analysis for this discrete series (e.g. time-series analysis). What's your experiences in this area?
The approach you've mentioned---take snapshots, compute statistics and then analyze the time series---has indeed attract many researchers, including me. I've used this approach to learn time series models from dynamic graphs in order to compare different dynamic graphs with each other:
https://www.researchgate.net/publication/224850368_Analysis_of_Dynamic_Brain_Networks_using_VAR_Models
Another way to work with these graphs is to learn graph models, e.g. from Barabasi or Watts-Strogatz, to analyze the dynamics. It basically depends where your graph comes from and what you want to do with it.
Conference Paper Analysis of Dynamic Brain Networks using VAR Models
Comparing snapshots, over time, is an effective way of watching the emergent structure of a network. Just be careful not to make the time slices too small. As an example, your network may look totally different, day-to-day, or weekly, but monthly or yearly you will see the larger patterns of change. Social and work network evolve gradually(+ and -) unless you move to a new city or change jobs.
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