A method for executing a query on a graph data stream. The graph stream comprises data representing edges that connect vertices of a graph. The method comprises constructing a plurality of synopsis data structures based on at least a subset of the graph data stream. Each vertex connected to an edge represented within the subset of the graph data stream is assigned to a synopsis data structure such that each synopsis data structure represents a corresponding section of the graph. The method further comprises mapping each received edge represented within the graph data stream onto the synopsis data structure which corresponds to the section of the graph which includes that edge, and using the plurality of synopsis data structures to execute the query on the graph data stream.