For matlab clustering, can centroid linkage work for distances other than Euclidean?

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If I am doing hierarchical clustering, if I am using centroid linkage with a distance function other than Euclidean, say, for example, minkowski distance with an exponent of 3 as opposed to 2, will that necessarily not work? What would matlab do if it was given centroid linkage and a Minkowski distance with an exponent fo 3 so that it was not simply Euclidean distance?

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You can use the linkage function define other distances. Examples are included in the link.