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For example, a path connected topological space is simply connected if each loop (path from a point to itself) in it is contractible; that is, intuitively, if there is essentially only one way to get from any point to any other point.
For example, in graph theory, a connected graph is one from which we must remove at least one vertex to create a disconnected graph.
The connectivity of a graph is the minimum number of vertices that must be removed, to disconnect it.