The principal end of this association must be explicitly configured using either the relationship fluent API or data annotations

by

Entity Framework Code-First conventions are assuming that EntityA.EntityB and EntityB.PreferredEntityA belong to the same relationship and are the inverse navigation properties of each other. Because both navigation properties are references (not collections) EF infers a one-to-one relationship.

Since you actually want two one-to-many relationships you must override the conventions. With your model it’s only possible with Fluent API:

modelBuilder.Entity<EntityA>()
    .HasRequired(a => a.EntityB)
    .WithMany()
    .HasForeignKey(a => a.EntityBID);

modelBuilder.Entity<EntityB>()
    .HasOptional(b => b.PreferredEntityA)
    .WithMany()
    .HasForeignKey(b => b.PreferredEntityAID);

(If you use this you can remove the [ForeignKey] attributes.)

You cannot specify a mapping that would ensure that the preferred child is always one of the associated childs.

If you don’t want to use Fluent API but only data annotations you can add a collection property in EntityB and relate it to EntityA.EntityB using the [InverseProperty] attribute:

public class EntityB
{
    public int ID { get; set; }
    public Nullable<int> PreferredEntityAID { get; set; }

    [ForeignKey("PreferredEntityAID")]
    public virtual EntityA PreferredEntityA { get; set; }

    [InverseProperty("EntityB")] // <- Navigation property name in EntityA
    public virtual ICollection<EntityA> EntityAs { get; set; }
}

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