Given a directed graph EE and an associative unital ring RR one may define the Leavitt path algebra with coefficients in RR, denoted by LR(E)LR(E). For an arbitrary group GG, LR(E)LR(E) can be viewed as a GG-graded ring. In this paper, we show that LR(E)LR(E) is always nearly epsilon-strongly GG-graded. We also show that if EE is finite, then LR(E)LR(E) is epsilon-strongly GG-graded. We present a new proof of Hazrat’s characterization of strongly Zℤ-graded Leavitt path algebras, when EE is finite. Moreover, if EE is row-finite and has no source, then we show that LR(E)LR(E) is strongly Zℤ-graded if and only if EE has no sink. We also use a result concerning Frobenius epsilon-strongly GG-graded rings, where GG is finite, to obtain criteria which ensure that LR(E)LR(E) is Frobenius over its identity component.