How Should I Declare Foreign Key Relationships Using Code First Entity Framework (4.1) in MVC3?

If you have an Order class, adding a property that references another class in your model, for instance Customer should be enough to let EF know there’s a relationship in there:

public class Order
{
    public int ID { get; set; }

    // Some other properties

    // Foreign key to customer
    public virtual Customer Customer { get; set; }
}

You can always set the FK relation explicitly:

public class Order
{
    public int ID { get; set; }

    // Some other properties

    // Foreign key to customer
    [ForeignKey("Customer")]
    public string CustomerID { get; set; }
    public virtual Customer Customer { get; set; }
}

The ForeignKeyAttribute constructor takes a string as a parameter: if you place it on a foreign key property it represents the name of the associated navigation property. If you place it on the navigation property it represents the name of the associated foreign key.

What this means is, if you where to place the ForeignKeyAttribute on the Customer property, the attribute would take CustomerID in the constructor:

public string CustomerID { get; set; }
[ForeignKey("CustomerID")]
public virtual Customer Customer { get; set; }

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EDIT based on Latest Code
You get that error because of this line:

[ForeignKey("Parent")]
public Patient Patient { get; set; }

EF will look for a property called Parent to use it as the Foreign Key enforcer. You can do 2 things:

1) Remove the ForeignKeyAttribute and replace it with the RequiredAttribute to mark the relation as required:

[Required]
public virtual Patient Patient { get; set; }

Decorating a property with the RequiredAttribute also has a nice side effect: The relation in the database is created with ON DELETE CASCADE.

I would also recommend making the property virtual to enable Lazy Loading.

2) Create a property called Parent that will serve as a Foreign Key. In that case it probably makes more sense to call it for instance ParentID (you’ll need to change the name in the ForeignKeyAttribute as well):

public int ParentID { get; set; }

In my experience in this case though it works better to have it the other way around:

[ForeignKey("Patient")]
public int ParentID { get; set; }

public virtual Patient Patient { get; set; }