Subject: Re: [arch-d] Thoughts about addresses, or why the overall architecture affects routing.

From: [email-masked] (Noel Chiappa)
Date: Sun, 19 Nov 2006 11:10:22 -0500 (EST)

> From: John Day <[email-masked]>

    > progress could be made if we were more careful about how use the word
    > "topology" and not use it when we mean "graph." 

We have fallen, for decades now, into the habit of using the term "topology"
to mean "connectivity pattern of network elements".

I hesitate to use the word "graph" there, as in "connectivity graph", because
a graph is, after all, merely a representation system, and one that doesn't
work well in some circumstances, e.g. a radio network. Classical node-and-arc
graphs are not well-suited to representing connectivity patterns in such
networks.

I don't think "topology" is entirely inappropriate terminology. For one, the
strict definition of "topology" ("properties of geometric figures or solids
that are not changed by homeomorphisms, such as stretching or bending") is
kind of apt, because network diagrams - and network routing - usually don't
care what the actual physical layout is, rather they only care what is
connected to what (which is, after all, basically the definition of the
topology of a geometric figure). E.g. the things you are interested in about
a particular connectivity pattern remain invariant if you "stretch or bend" a
graphical representation projected onto a plane. Also, the topology of some
object tells you about its properties, and the "topology" of the network's
connectivity pattern similarly tells you things about the network.

So, yes, I know it's not the canonical use of the term, but I think it's at
least as apt a word as any other non-neologism.

	Noel

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---

From: John Day <[email-masked]>
Date: Sun, 19 Nov 2006 11:49:40 -0500

>that are not changed by homeomorphisms, such as stretching or bending") is

The more formal definition states that the topology is the 
homeomorphism.  So my test as to when I use graph or topology is 
whether or not the thing I am talking about might be construed as a 
mapping between a set of graphs.  If not, then it is a graph.  If I 
could imagine a mapping (and I have a pretty good imagination!), then 
it is a topology.

>connectivity pattern similarly tells you things about the network.

Correct. See above.

>least as apt a word as any other non-neologism.

And there are times I want to use the difference.

Take care,
John