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In the definition of a network, are we only considering connected graphs ?

Because I keep encountering definitions that don't assume explicitly that we deal with connected graphs, but which would be very counter-intuitive if they would also apply for disconnected graphs (almost everywhere one is advised to think of a network - the mathematical object - as a network of pipes transporting some fluid; if disconnected graphs come into play this metaphor of pipes transporting something fails!).

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    "Network" means different things to different people. What context is this in?2011-07-22
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    If you mean computer networks, they do not have to be connected. You might want the graph to be [weighted](http://en.wikipedia.org/wiki/Weighted_graph#Weighted_graphs_and_networks) or [directed](http://en.wikipedia.org/wiki/Weighted_graph#Direction), depending on the situation (network characteristics and problem at hand).2011-07-22
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    @Qiaochu Well, there isn't much context; I was just confronted with *networks* during a course in discrete mathematics, where also some graph-theoretical topics were treated. Basically we just got the definition and some lemmas and theorems followed that illustrated some properties of the definitions and then we moved on to other topics. We defined a *network* to be a directed graph (@ Emre, sorry, should have mentioned that earlier), that contains to two special nodes, the source and the sink, and a function (the capacity) $f:E\rightarrow \mathbb{R}$.2011-07-23
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    Also (@ Qiaochu) what would be all the other meanings *network* ?2011-07-23
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    @resu: I don't know. All I'm saying is that a lot of people use the word "network" (computer scientists, biologists, social scientists, etc.) and I would be rather surprised if their usages matched exactly. It doesn't, to my knowledge, have a precise, agreed-upon mathematical definition, and before you gave that definition that I thought you were referring to a graph.2011-07-23
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    @resu: ah, it looks like the term I'm slightly more familiar with is _flow_ network: http://en.wikipedia.org/wiki/Flow_network Anyway, I know it's hard to tell whether a definition is standard or not, but when in doubt please include all of the definitions you're using.2011-07-23

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