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let R Relation: (u,v) in R iff there is a path between u and v (u and v are graph vertices)

I want to prove that Relation R is transitive, now i've seen than you cant just concatenate Pu->v to Pv->w and you have to cut those pathes at their meeting and only then concatenate.

my question is, why is that?

Thanks.

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    Do you know what "path" means?2012-09-26
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    yeah, it meens that there is a sequence of vertices such that from each of its vertices there is an edge to the next vertex in the sequence.2012-09-26
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    A path is a trail in which all vertices (except perhaps the first and last ones) are distinct.2012-09-26
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    @Some1Pr0 vertices must be distinct!2012-09-26
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    why? there is **simple path** which is a distincted **path**2012-09-26

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