Due to enormous complexity of the unstructured peer-to-peer networks as large-scale, self-configure, and dynamic systems, the models used to characterize these systems are either inaccurate, because of oversimplification, or analytically inapplicable, due to their high complexity. By recognizing unstructured peer-to-peer networks as "complex systems", we employ statistical models used before to characterize complex systems for formal analysis and efficient design of peer-to-peer networks. We provide two examples of application of this modeling approach that demonstrate its power. For instance, using this approach we have been able to formalize the main problem with normal flooding search, propose a remedial approach with our probabilistic flooding technique, and find the optimal operating point for probabilistic flooding rigorously, such that it improves scalability of the normal flooding by 99%.