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The scipy dendrogram documentation says:

dendrogram(Z, ...)
    The dendrogram illustrates how each cluster is
    composed by drawing a U-shaped link between a non-singleton
    cluster and its children. ...It is expected that the distances in Z[:,2] be
    monotonic, otherwise crossings appear in the dendrogram.

I'm unclear about the sentence about "It is expected that the distances in Z[:,2] be monotonic, otherwise crossings appear in the dendrogram"? What crossing in the diagram is referred to? Can someone please show an example where this happens for a particular distance matrix with an explanation of why?

Is this an example of a crossing? seems to me this arises just by some symmetries in distance matrix... enter image description here

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Z is supposed to specify merges of clusters (which 2 clusters are merged) and the "time" they happen, where "time" is the y-axis of the dendrogram (this is what they mean by distances). Z is usually constructed so that "time" is in increasing order, which also makes it easy to plot so that U shapes are not on top of each other. If you plot the U's in a different order, they may overlap each other and it will looked messed up - that is what is referred to as crossings.

I ran a short example, this is an example of what a crossing will look like:

enter image description here

Bottom line: stick with the correct order.

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not sure I follow still.. I added an example. Is that considered a crossing?
@user248237dfsf I added an example. Just follow the manual guidelines and you will be fine.
@user248237dfsf I don't think so. Looks like it just happens at the same "time".

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