I want to understand why we use the term "network topology" as opposed to "network graph", or another term, to talk about the structure of networks. I'm working on a network design for a project, and want to make sure I don't use any terms that I don't truly understand.

Wikipedia defines network topology as "the arrangement of the various elements (links, nodes, etc.) of a computer network." This strikes me as interesting, because when I hear the words link and node, I immediately think of graph theory and the objects it is concerned with.

Topology, according to Wikipedia again, is "concerned with the properties of space that are preserved under continuous deformations..." And when you look at the basic examples of topological objects, you see coffee cups and Möbius strips, as opposed to the discrete vertices and edges you see with graph theory.

So why do we refer to networks as having a "topology"?

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    I'm voting to close this question as off-topic because it is about language terminology – GlenH7 Jan 12 '16 at 15:32
  • @GlenH7 Any idea which SE would be a good fit for it? – GladstoneKeep Jan 12 '16 at 16:01
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    @GlenH7: call me nitty, but this question is about a technical term. Such questions are on-topic for Programmers, if the term in stake is a conceptual programming term. "Network topology" sounds more like a hardware-related term to me, but I think the topic also touches a lot of conceptual programming questions. Might be an edge-case. – Doc Brown Jan 12 '16 at 18:18

Topology is the study of fundamental properties that exist no matter the arrangement of elements (for example the ratio of points, edges and faces in a polygon that does not change as you add or reduce points).

This term fits networks well because what you are looking for with network topology is the different arrangements of the network to perform the same function, with the goal being to produce the simplest configuration that you can to perform the task (thus eliminating waste)

A graph has a much more limited definition in mathematics and is not really about discovering the fundamental properties of arrangements.

  • So you think there is a "real" reason for the term "network topology" beeing used more frequently than "network graph"? I doubt that. – Doc Brown Jan 13 '16 at 14:59
  • Maybe it just sounds cool :-) Here is a good discussion on difference between graphs and topology math.stackexchange.com/questions/520768/… – Cormac Mulhall Jan 13 '16 at 16:27
  • I added that first remark of yours to my answer, I can imagine that is indeed the "real reason" ;-) – Doc Brown Jan 13 '16 at 17:35

Each graph is a topological object. The main properties of a graph are the nodes as well as the links between them. Those are properties which are preserved under continuous deformations. Thus the term "network graph" can surely be used in exchange for "network topology". The latter is probably more widely used; it highlights the "topological" properties a network like "which node is connected to which other node(s)", whilst ignoring properties like line length, band-width or other "non-topological" / "non-graph" properties.

However, I am pretty sure that has simply historical reasons, and not because it really fits better in a mathematical sense. And maybe "network topology" just sounds "more cool" to a lot of people than "network graph", as @CormacMullhall wrote in his comment ;-)

  • Cool, that clears up a lot. I didn't realize that graphs fell under the umbrella of topology, but that makes sense. – GladstoneKeep Jan 13 '16 at 14:59

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