A system for querying a graph model and methods for making and using same. An initial vertex set can be received for one or more query blocks. The one or more query blocks can be executed to generate respective output vertex sets. The output vertex sets and the initial vertex set can be enabled to interconnect in a vertex-set-flow graph based on the query blocks. The vertex-set-flow graph can have a Directed Acyclic Graph shape. A selected query block can generate an output vertex set based on an input vertex set with or without traversal over an edge. A selected query block can calculate a runtime attribute. Edges and/or vertices of the graph model can be updated during querying. A selected block can call a graph query as a generic function. Functions for querying the graph model are powerful and can advantageously meet various graph query needs.