I am trying to inset data in a jena fuseki graph using this simple query:
PREFIX test:
INSERT {?subject test:hasName \"Bob\"}
WHERE
Make sure you are pointing at the appropriate endpoint. In Fuseki the queries endpoint (for example, http://localhost:13030/mygraph/query) is different than the update endpoint (http://localhost:13030/mygraph/update).
Selects, asks and constructs should be done using the first one, while updates, inserts and deletes should be done using the second one.