':return: The length of the shortest hypernym path from this
synset to the root.'

def min_depth(self):

    if (u'_min_depth' not in self.__dict__):
        hypernyms = (self.hypernyms() + self.instance_hypernyms())
        if (not hypernyms):
            self._min_depth = 0
        else:
            self._min_depth = (1 + min((h.min_depth() for h in hypernyms)))
    return self._min_depth
