Three categories of mathematical model on Network

From Networkbiology.net

1. Direct studies of the real-world networks themselves, measuring various properites such as degree-distribution, diameter, clustering, etc. 
2. Suggestions for new random graph models motivated by this study
3. computer simulations of the new models, measuring their properites.
4. heuristic analysis of the new models to proedict their properties
5. Rigorous mathematical study of the new models, to prove theorems about their properties. 

(From Handbook of Graphs and Network from the Genome to the Internet by Stefan Bornholdt, and Heinz Georg Schuster)