Having given it more thought I decided that a hierarchy doesn't have to be 
a tree. A tree is a diagram or graph that branches from a single stem 
without forming loops or polygons.

A hierarchy could have "loops" or "polygons." In other words, there could 
be more than one way to get between layers in the hierarchy. Think of the 
dotted lines we so often see on org charts.

When you look at examples of Cisco's hierarchical design, in most cases 
they aren't actually trees. There are, of course, redundant ways to get 
between layers.

Hierarchy just implies layers and that each layer has a particular job and 
ranking. I don't think it has a mathematical meaning. In fact (and Howard 
will like this because it goes with his 7 deadly sins ;-) most of the 
meanings for hierarchy have to do with the church:

1 a division of angels
2 a ruling body of clergy organized into orders or ranks each subordinate 
to the one above it; especially : the bishops of a province or nation b : 
church government by a hierarchy

So, it was an off-the-wall comment that made sense when in a hurry and not 
when given some thought.

(Although a lot of systems analysis techniques do assume that hierarchy 
means tree!??) Did anyone every use IBM's HIPO method: Hierarchy, Input, 
Process, Output. It worked extremely well. I don't think it would let you 
use a hierarchy that wasn't also a tree, although I can't remember for sure.

Priscilla

At 12:17 PM 10/23/01, Jonathan Hays wrote:
>Not being trained in topological mathematics  I am geussing that you are
>telling us
>that there are other common hierarchical forms. The tree is the only one I
>hear about.
>What are the others you have in mind?
>
>Priscilla Oppenheimer wrote:
>
> > I was hoping nobody would answer. ;-) Because actually I don't like my
> > answer. It should read, "A hierarchical network design MAY already be a
> > tree!" It wouldn't necessarily be a tree.
> >
> > Priscilla
________________________

Priscilla Oppenheimer
http://www.priscilla.com




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