Which of the following services is considered a fully managed graph database service?

Amazon Neptune is recognized as a fully managed graph database service specifically designed for handling highly connected data. It supports both the Property Graph model and the RDF (Resource Description Framework) model, which allows users to seamlessly build and query sophisticated graph structures, making it ideal for applications like social networking, recommendation engines, and fraud detection.

As a fully managed service, Amazon Neptune takes care of routine database management tasks such as hardware provisioning, patching, backup, recovery, and scaling, allowing developers to focus on building applications without needing to manage the underlying infrastructure.

In contrast, the other options are not dedicated graph database services. Amazon Redshift is primarily an analytical data warehouse, Amazon Aurora provides a relational database compatible with MySQL and PostgreSQL, and Amazon RDS is a managed relational database service that supports several database engines but does not offer graph database capabilities in the way Neptune does. Thus, the unique features and management capabilities of Amazon Neptune clearly establish it as the correct answer.