The Freebase API is an open source knowledge graph that contains the public part of the knowledge base that Google uses to populate a list of related queries.
It is actually released by Google, however it only contains a subset of the full knowledge graph due to legal restrictions from some data sources.
Search results can be requested programmatically using HTTP and JSON, or various programming languages ββexist.
Here is the default JSON result for the "clooney" example asked in the question. Which can be filtered through the API and used as a seed for branching the search, depending on the usecase.
norlesh
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