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This question is with regards to terminology. I am writing a journal paper that describes the software I develop at my workplace call Navigator. The software is used for visualization of networks/graphs. At work, we commonly interchange the use of the words 'networks' and 'graphs' to refer to the same concept. But for writing the journal paper, I would like to know if they can be safely interchanged, or if they refer to slightly different concepts?

The software is used for modeling arbitrary entities as nodes and arbitrary connections between them as edges between the nodes. The graphs are not directed. No flow is implied, but some idea of flow can be added by attaching numerical/textual attributes to the edges.

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In the graph-theory-article on Wikipedia you can read "A digraph with weighted edges in the context of graph theory is called a network." – Daniel Krenn Nov 2 '10 at 15:40
My experience is that "network" and "graph" are both quite overloaded. Whichever one you choose, define it carefully. – Qiaochu Yuan Nov 2 '10 at 15:47
Use whichever terminology your target audience is more familiar with. The point of writing is not pedantry, but communication. – Boris Bukh Nov 3 '10 at 14:15
up vote 2 down vote accepted

If someone says "graph" without further specification I consider it to mean an unweighted undirected graph without loops or multiple edges. I consider "network" to be a more general term. Especially if the audience of the article is more on the applied side, I would go with network.

But really in your situation I would poke through some other NAViGaTOR papers, particularly Igor Jurisica's, and see what he uses. I bet it will be "network" almost all the time.

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Isolated fact and opinions:

In MAPLE the package for working with graphs was called networks. One could (and still can) say something like new(G) advertex({1,2,3},G) addedge({{1,2},[2,3]},G): the last adding an undirected edge {1,2} and a directed edge [2,3]. but one could also say G:=graph({1,2,3},{{1,2},[2,3]}}: However that package has been deprecated and the current one is GraphTheory.

I think of a graph as more abstract and a network as a graph which is more specific such as the interstate highway system, the people I know on facebook or the computers in my house. When a graph gets values put on its edges (like a certain flow) it gets to be more networky.

In short I agree with Andrew. You can use either, just study your audience and be clear.

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I worked at a telecommunications equipment company for several years, and although there was no hard-and-fast distinction between "graph" and "network," I would say that we tended to use "graph" for an abstract mathematical object and "network" for something whose nodes had some kind of physical existence.

It sounds to me that your software deals with entities that are on the abstract end of the spectrum, so I would tend to call them graphs. "Network" may carry a connotation that your software is used for designing specific kinds of physical networks, such as telephone networks, road networks, etc.

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