  An association scheme is called amorphic if every possible fusion of
relations gives rise to a fusion scheme. We call a pair of relations fusing if
fusing that pair gives rise to a fusion scheme. We define the fusing-relations
graph on the set of relations, where a pair forms an edge if it fuses. We show
that if the fusing-relations graph is connected but not a path, then the
association scheme is amorphic. As a side result, we show that an association
scheme in which at most one relation is not strongly regular of (negative)
Latin square type, is amorphic.
