implement GetHashCode() for objects that contain collections

Question

Consider the following objects:

class Route
{
   public int Origin { get; set; }
   public int Destination { get; set; }
}

Route implements equality operators.

class Routing
{
   public List<Route> Paths { get; set; }
}

I used the code below to implement GetHashCode method for the Routing object and it seems to work but I wonder if that's the right way to do it? I rely on equality checks and as I'm uncertain I thought I'll ask you guys. Can I just sum the hash codes or do I need to do more magic in order to guarantee the desired effect?

public override int GetHashCode() =>
{
    return (Paths != null 
                ? (Paths.Select(p => p.GetHashCode())
                        .Sum()) 
                : 0);
}

I checked several GetHashCode() questions here as well as MSDN and Eric Lippert's article on this topic but couldn't find what I'm looking for.

Answer 1

I think your solution is fine. (Much later remark: LINQ's Sum method will act in checked context, so you can very easily get an OverflowException which means it is not so fine, after all.) But it is more usual to do XOR (addition without carry). So it could be something like

public override int GetHashCode()
{
  int hc = 0;
  if (Paths != null)
    foreach (var p in Paths)
      hc ^= p.GetHashCode();
  return hc;
}

Addendum (after answer was accepted):

Remember that if you ever use this type Routing in a Dictionary<Routing, Whatever>, a HashSet<Routing> or another situation where a hash table is used, then your instance will be lost if someone alters (mutates) the Routing after it has been added to the collection.

If you're sure that will never happen, use my code above. Dictionary<,> and so on will still work if you make sure no-one alters the Routing that is referenced.

Another choice is to just write

public override int GetHashCode()
{
  return 0;
}

if you believe the hash code will never be used. If every instace returns 0 for hash code, you will get very bad performance with hash tables, but your object will not be lost. A third option is to throw a NotSupportedException.