Entity Framework Many to Many Relation on same entity with additional parameters - entity-framework

Question

I have City entity:
public class City
{
public int ID { get; set; }
public string Name { get; set; }
public virtual ICollection<CityDistance> CityDistances { get; set; }
}
and i would like to keep distances between cities.
1. How can achieve this in code first entity framework 6?
Here are my other classes:
public class CityDistance
{
[Key, Column(Order = 0)]
public int CityAID { get; set; }
[Key, Column(Order = 1)]
public int CityBID { get; set; }
public virtual City CityA { get; set; }
public virtual City CityB { get; set; }
public double Distance { get; set; }
}
Is this correct design?
When i run "add-migration Distances" here is the result.
3. Why is it adding another foreign key column named "City_ID"?
CreateTable(
"dbo.CityDistances",
c => new
{
CityAID = c.Int(nullable: false),
CityBID = c.Int(nullable: false),
Distance = c.Double(nullable: false),
City_ID = c.Int(),
})
.PrimaryKey(t => new { t.CityAID, t.CityBID })
.ForeignKey("dbo.Cities", t => t.City_ID)
.ForeignKey("dbo.Cities", t => t.CityAID, cascadeDelete: true)
.ForeignKey("dbo.Cities", t => t.CityBID, cascadeDelete: true)
.Index(t => t.CityAID)
.Index(t => t.CityBID)
.Index(t => t.City_ID);

Answer 1

That's because EF is acting like a simple bookkeeper: CityA, CityB, that's two foreign keys, CityDistances, that's another foreign key, that makes three foreign keys.
EF doesn't know that you intend CityDistances to be the other (inverse) end of the association for either CityA or CityB. You have to indicate this explicitly, either by data annotations:
public class City
{
...
[InverseProperty("CityA"]
public virtual ICollection<CityDistance> CityDistances { get; set; }
}
or by fluent mapping:
modelBuilder.Entity<City>()
.HasMany(c => c.CityDistances)
.WithRequired(cd => cd.CityA)
.HasForeignKey(cd => cd.CityAID);
(By which I implicitly say that, yes, this is correct design, at least technically).