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 for connected graph
From The Free On-line Dictionary of Computing (30 December 2018) :

  connected graph
      A graph such that there is a path between any
     pair of nodes (via zero or more other nodes).
     Thus if we start from any node and visit all nodes connected
     to it by a single edge, then all nodes connected to any of
     them, and so on, then we will eventually have visited every
     node in the connected graph.

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