The primitive ideal space of the $C^{*}$-algebras of infinite graphs

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For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).

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Kumjian-Pask algebras of higher-rank graphs (2011, methodology): “The parametrization of ideals in Cuntz-Krieger algebras by the saturated hereditary subsets comes from [11], and was extended to various classes of graph C∗-algebras in [23, 9, 8, 18].”
The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆ (2013, background): “A gem in this program is Hong and Szymański’s description [9] of the primitive ideal space of the C∗-algebra of a directed graph.”
Remarks on some fundamental results about higher-rank graphs and their C*-algebras (2011, background): “C∗-algebras associated to graphs and k-graphs have attracted significant attention recently because they at once encompass a great many interesting examples [2, 6, 11, 17], and are remarkably tractable [3, 4, 5, 7, 12, 13, 21].”
Stable rank of graph algebras. Type I graph algebras and their limits (2002, background): “As explained in [ 7 ], the maximal tails in Mγ(E) give rise to gauge-invariant primitive ideals of C ∗ (E), while those in Mτ(E) to”
Gauge-Invariant Ideals in the C*-Algebras of Finitely Aligned Higher-Rank Graphs (2004, background): “in [ 3 ]. The results of [2] were obtained by a process which builds from a graph E and a gauge-invariant ideal I in C ∗(E), a new graph F = F(E, I) in such a way that the graph C ∗-algebra C ∗(F) is canonically isomorphic to the quotient algebra C ∗(E)/I.”