On Thu, 2009-02-19 at 22:57 +1100, Timothy S. Nelson wrote:
> On Thu, 19 Feb 2009, Carl Mäsak wrote:
> > A tree is a graph without cycles.

That's insufficient.  In fact, there are a number of ways that the
general concept of an acyclic graph must be constrained before you get
something you can call a 'tree'.

> > The concept of a "root" is very common in computer representations, but in 
> > no way necessary for a general tree. In fact, in phylogenetics, it's 
> > business as usual to handle unrooted trees. This makes the $root attribute 
> > meaningless in at least some cases.
>       Interesting.  I'm happy to assume that $root is allowed to be 
> Undefined, I think.  But let me ask a question; were you to represent an 
> unrooted tree in a computer, how would you do it so that, if you had to look 
> around the tree, you could do it?  You'd need some node that was an 
> entry-point into the tree.  That's the purpose I'm trying to get at here.

A tree with nodes but without a root is not a tree -- it's a collection
of trees, more commonly called a grove or forest.


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