1. A live topological query method performed by a physical computing system, the method comprising: with a querying application, using a query graph to create a live topological query result from a database storing a full structure graph while not storing an entirety of said query result in a cache memory; in response to detecting a change within said full structure graph, performing a calculation to determine whether said change is relevant to said query result; and notifying said querying application of a relevant change to said query result without relying on a fully cached copy of said query result.