Using the Steinberg algebra model to determine the center of any Leavitt   path algebra
  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. 
Lisa Orloff Clark, Dolores Mart\'in Barquero, C\'andido Mart\'in   Gonz\'alez and Mercedes Siles Molina
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