Is the microsoft graph API available with on-premise installations? If yes 2013, 2016?
I don't think Microsoft Graph API will be available for on-premises. Microsoft graph is part of Azure infrastructure and does not know anything about your local environment. To use Graph API you need to register an App in Azure AD. With an on-premises environment you can't perform this step since you are not connected to Azure AD in any way.
Microsoft Graph exposes multiple APIs from Office 365 and other Microsoft cloud services through a single endpoint: https://graph.microsoft.com.
Access data from multiple Microsoft cloud services, including Azure Active Directory, Exchange Online as part of Office 365, SharePoint, OneDrive, OneNote, Planner and Microsoft Teams.
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