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