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Tree words are infinite words that are defined in terms of extension graphs that describe the left and right extensions of their factors; tree words are such that their extension graphs are trees. This class of words includes classical families of words such as Sturmian and episturmian words, codings of interval exchanges or else Arnoux-Rauzy words. We investigate here the properties of substitutive tree words and prove some rigidity properties, that is, algebraic properties on the set ofdoi:10.1142/s0129054118420017 fatcat:ljboyxp46ndfhgfvq265kt6sr4