If you connect Microsoft Visio 2013 to a Microsoft SQL Server LocalDb instance by using the standard (localdb)\V11.0 instance name, you might get the error:

[DBNETLIB][ConnectionOpen (Connect()).]SQL Server does not exist or access denied.

To fix this error use the following instance name: np:\\.\pipe\LOCALDB#92FE49CE\tsql\query

The number in bold can be found in the Microsoft SQL Server Management Studio 2012 Server Properties dialog, when connected to the (localdb)\V11.0 instance: