[c#] LINQ to read XML

I got this XML file:

<root>
    <level1 name="A">
        <level2 name="A1" />
        <level2 name="A2" />
    </level1>
    <level1 name="B">
        <level2 name="B1" />
        <level2 name="B2" />
    </level1>
    <level1 name="C" />
</root>

Could someone give me a C# code using LINQ, the simplest way to print this result:
(Note the extra space if it is a level2 node)

A
  A1
  A2
B
  B1
  B2
C

Currently I got this code:

XDocument xdoc = XDocument.Load("data.xml"));
var lv1s = from lv1 in xdoc.Descendants("level1")
           select lv1.Attribute("name").Value;

foreach (var lv1 in lv1s)
{
    result.AppendLine(lv1);

    var lv2s = from lv2 in xdoc...???
}

XDocument xdoc = XDocument.Load("data.xml");
var lv1s = xdoc.Root.Descendants("level1"); 
var lvs = lv1s.SelectMany(l=>
     new string[]{ l.Attribute("name").Value }
     .Union(
         l.Descendants("level2")
         .Select(l2=>"   " + l2.Attribute("name").Value)
      )
    );
foreach (var lv in lvs)
{
   result.AppendLine(lv);
}

Ps. You have to use .Root on any of these versions.

Here are a couple of complete working examples that build on the @bendewey & @dommer examples. I needed to tweak each one a bit to get it to work, but in case another LINQ noob is looking for working examples, here you go:

//bendewey's example using data.xml from OP
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Xml.Linq;

class loadXMLToLINQ1
{
    static void Main( )
    {
        //Load xml
        XDocument xdoc = XDocument.Load(@"c:\\data.xml"); //you'll have to edit your path

        //Run query
        var lv1s = from lv1 in xdoc.Descendants("level1")
           select new 
           { 
               Header = lv1.Attribute("name").Value,
               Children = lv1.Descendants("level2")
            };

        StringBuilder result = new StringBuilder(); //had to add this to make the result work
        //Loop through results
        foreach (var lv1 in lv1s)
        {
            result.AppendLine("  " + lv1.Header);
            foreach(var lv2 in lv1.Children)
            result.AppendLine("    " + lv2.Attribute("name").Value);
        }
        Console.WriteLine(result.ToString()); //added this so you could see the output on the console
    }
}

And next:

//Dommer's example, using data.xml from OP
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Xml.Linq;

class loadXMLToLINQ
{
static void Main( )
    {
        XElement rootElement = XElement.Load(@"c:\\data.xml"); //you'll have to edit your path
        Console.WriteLine(GetOutline(0, rootElement));  
    }

static private string GetOutline(int indentLevel, XElement element)
    {
        StringBuilder result = new StringBuilder();
        if (element.Attribute("name") != null)
        {
            result = result.AppendLine(new string(' ', indentLevel * 2) + element.Attribute("name").Value);
        }
        foreach (XElement childElement in element.Elements())
        {
            result.Append(GetOutline(indentLevel + 1, childElement));
        }
        return result.ToString();
    }
}

These both compile & work in VS2010 using csc.exe version 4.0.30319.1 and give the exact same output. Hopefully these help someone else who's looking for working examples of code.

EDIT: added @eglasius' example as well since it became useful to me:

//@eglasius example, still using data.xml from OP
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Xml.Linq;

class loadXMLToLINQ2
{
    static void Main( )
    {
        StringBuilder result = new StringBuilder(); //needed for result below
        XDocument xdoc = XDocument.Load(@"c:\\deg\\data.xml"); //you'll have to edit your path
        var lv1s = xdoc.Root.Descendants("level1"); 
        var lvs = lv1s.SelectMany(l=>
             new string[]{ l.Attribute("name").Value }
             .Union(
                 l.Descendants("level2")
                 .Select(l2=>"   " + l2.Attribute("name").Value)
              )
            );
        foreach (var lv in lvs)
        {
           result.AppendLine(lv);
        }
        Console.WriteLine(result);//added this so you could see the result
    }
}

Or, if you want a more general approach - i.e. for nesting up to "levelN":

void Main()
{
    XElement rootElement = XElement.Load(@"c:\events\test.xml");

    Console.WriteLine(GetOutline(0, rootElement));  
}

private string GetOutline(int indentLevel, XElement element)
{
    StringBuilder result = new StringBuilder();

    if (element.Attribute("name") != null)
    {
        result = result.AppendLine(new string(' ', indentLevel * 2) + element.Attribute("name").Value);
    }

    foreach (XElement childElement in element.Elements())
    {
        result.Append(GetOutline(indentLevel + 1, childElement));
    }

    return result.ToString();
}

A couple of plain old foreach loops provides a clean solution:

foreach (XElement level1Element in XElement.Load("data.xml").Elements("level1"))
{
    result.AppendLine(level1Element.Attribute("name").Value);

    foreach (XElement level2Element in level1Element.Elements("level2"))
    {
        result.AppendLine("  " + level2Element.Attribute("name").Value);
    }
}