A search engine queries a network model for behavior of the entire network, such as data flow, based on combinations of multiple network elements. The search engine provides the state information and/or predicted behavior of the network by searching network objects in a graph-based model or a network state database that satisfy constraints given in a search query. The search engine provides the state information and/or predicted behavior based on regular-expression or plain language search expressions that do not provide packet header information. The search engine parses such search expression into a sequence of atoms that encode forwarding paths of interest to the user. A flow path through the modeled network can be generated dynamically, within the context of the search queries.