Summary: We investigate the information implied by the form of the Adian graphs of semigroup presentation of the form \(P=\langle a_1,a_2,\dots,a_n\mid w_1=a_1,\;w_2=a_2,\dots,w_n=a_n\rangle\). In particular, we show that if \(P\) defines a monoid then both the left and right Adian graphs of \(P\) are connected.