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This gets more complicated with directed graphs.
connected($start, $end, $directed=TRUE) - have to find if a path exists between things, real adjacency matrix can speed this up
graphConnected($directred=TRUE) - works on the whole graph (first check minimum degree then do expensive stuff).
weaklyConnected($start, $end) - real adjacency matrix can speed this up. Slightly ambiguous, if a directed graph is connected between two points it is also weakly connected.
see http://en.wikipedia.org/wiki/Connected_graph for some more information
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