# Are 2 diagram homeomorphic?

Indeed there are many way to prove whether something are homeomorphic with each other. For the diagram below, it seems that they are not homeomorphic but i am not sure how to argue that.

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Removing the central point of the second diagram leaves a set with $6$ connected components; there is no point in the first diagram that has that property, and it is a topological property (i.e., one preserved by homeomorphisms).
@Clayton: Yes, that would also work: $4$ non-cut-points in the one, $6$ in the other (assuming that the line segments are closed). – Brian M. Scott Dec 14 '12 at 5:41