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I know the term for a group of trees is a "forest", but what is the term for a group of graphs?

The difference between a graph and a tree is that a tree can have no cycles, and usually has a node specified as the "root".

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    $\begingroup$ Well... technically, "group of graphs" is naturally a graph, while there is no obvious way to view "group of trees" as a tree. I'd be surprised if there was a distinct name for group of graphs. $\endgroup$ Commented Apr 28, 2014 at 16:25

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What you are thinking of as a "graph" is actually a connected graph. In general, a graph need not be connected, i.e. it could have many distinct parts which are all separate, called its "connected components".

The analagous statement to "a colection of trees is a forest" is "a collection of connected graphs is a graph."

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It's a graph. In fact, a forest is a graph too, not a group of graphs. It's just that a forest isn't a connected graph. The individual connected parts of a single graph are called components. Technically what you're calling a "group of graphs" is a graph, and what you're calling a "graph" is a connected graph.

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