Tree structure with reference to root in Entity Framework

I'm trying to model a tree structure for orders in Entity Framework. Right now I've go the following:

public class ProjectModel
{
    [Key]
    public int Id { get; set; }

    [Required]
    public string Name { get; set; }

    [Required]
    public int CustomerId { get; set; }

    public virtual List<ProjectNode> Nodes { get; set; }
}

public class ProjectNode
{
    [Key]
    public int Id { get; set; }

    [Required]
    public string Name { get; set; }

    public string Path { get; set; }

    public int? ParentId { get; set; }

    [ForeignKey("ParentId")]
    public virtual List<ProjectNode> Children { get; set; }
}

What I need to be able to do is get a reference to the root ProjectModel at any level of ProjectNode in order to authorize a given user actually having permission to view and change the project which contains the ProjectNode.

public class ProjectNode {
    public int ProjectId { get; set; }  //<-- this
...

public class ProjectModel {
    [Key]
    public int Id { get; set; }         //<-- containing the value of this
}

My question is whether its possible to have a theoretical ProjectId property populated at every level of the tree structure, or if I need to set it manually.

I had something working that at first blush appeared to allow this functionality, but upon further investigation only populated the ProjectId for ProjectNodes contained in the ProjectModel's Nodes property.

It seems to me like it would be super inefficient to recurse backwards through the structure to get to the root.