The idea of auxiliary random variable (r.v.) plays a very important role in characterizing the capacity of channels, especially in multi-user setting such as Gelfand-Pinsker or the degraded broadcast channel. In many cases, choosing a sequence of an i.i.d auxiliary r.v. allows us to simplify a capacity expression to have a computable, single-letter form. In this talk we will introduce a new kind of auxiliary r.v. that is not i.i.d. but has a memory that is generated on a graphical structure. In particular, we show that the feedback capacity of the unifilar channel is upper bounded by a single-letter expression that is a function of the stationary distribution on the graph representing the memory of the auxiliary r.v.. Furthermore, in all cases where the capacity is known, such as the trapdoor channel, Ising channel, Dicode channel, erasure channel with no repeated ones, the upper bound yields, with a small cardinality bound on the structured auxiliary r.v. , a tight bound on the feedback capacity.