A system for automatically updating saved query results for a graph responsive to a graph update is disclosed. The system may identify a target constraint responsive to an update to the data graph. The system may use an index of constraints organized by edge. The target constraint specifies a path in a data graph that includes an edge specified in the update. The system may determine a state for the target constraint by traversing the graph via the path and determine based on the state, whether a member node represents a change to the saved query result. The system may then update a saved query result for the query using the member node identified during the traversal in accordance with the change.