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Given an arbitrary graph, we describe the center of its Leavitt path algebraover a commutative unital ring. Our proof uses the Steinberg algebra model ofthe Leavitt path algebra. A key ingredient is a characterization of compactopen invariant subsets of the unit space of the graph groupoid in terms of theunderlying graph: an open invariant subset is compact if and only if itsassociated hereditary and saturated set of vertices satisfies Condition (F). Wealso give a basis of the center. Its cardinality depends on the number ofminimal compact open invariant subsets of the unit space.

Using the Steinberg algebra model to determine the center of any Leavitt path algebra