Ultragraphs give rise to labelled graphs. We realize algebras associated to such labelled graphs as groupoid algebras, generalizing a known groupoid algebra realization of ultragraph C*-algebras to any ultragraph. Then, we characterize the shift space of an ultragraph as the tight spectrum of the inverse semigroup associated with an ultragraph via its labelled graph. In the purely algebraic setting, we show that the algebraic partial action used to describe an ultragraph Leavitt path algebra as a partial skew group ring is equivalent to a dual of a topological partial action, and we use this to describe ultragraph Leavitt path algebras as Steinberg algebras. Finally, we prove generalized uniqueness theorems for both ultragraph C*-algebras and ultragraph Leavitt path algebras and characterize their abelian core subalgebras.

超声检查产生标记的图形。我们实现了与诸如带组图代数之类的标记图相关的代数，将超图C *-代数的已知带组代数实现推广到任何超图。然后，我们通过标记的图将超图的移位空间表征为与超图关联的逆半群的紧谱。在纯代数环境中，我们证明了将超图Leavitt路径代数描述为偏偏群环的代数部分作用等同于拓扑局部作用的对偶，并且我们用它来将超图Leavitt路径代数描述为Steinberg代数 最后，我们证明了超图C *-代数和超图Leavitt路径代数的广义唯一性定理，并刻画了它们的阿贝尔核子代数。