Facebook provides developers a set of APIs which helps us develop dynamic applications to integrate with Facebook Graph. This API presents a simple, consistent view of the facebook social Graph uniformly representing objects in the Graph (People, photos, pages) and the connection between them.
The graph API allows you to access all public information about the object. For additional information about users you need their permission. With this API we can develop applications to read from Android data into facebook.
Facebook authentication enables applications to interact with the Graph API on behalf of Facebook users and it provides a single sign in mechanism across web and mobile applications.
The Open Graph Protocol enables developers to integrate their web pages into social graph. It makes your pages equivalent to a Facebook page. Users can add your pages to their likes and interests and you have the ability to publish update to the users.
The Open Graph may have much wider implications on the web providing a different concept of Social Search Engine. With this Facebook is trying to connect the Open Graph to the rest of the world and provide a highly interactive version of Search Engine.