This is an answer to the question: *"Given a $C^\ast$-algebra $A$ that shares some properties of (higher-rank) graph algebras (such as separability, nuclearity, UCT, K-theoretic properties), can I conclude that $A$ **is** a (higher-rank) graph algebra?"*

My answer is: this would require a classification of the class of $C^\ast$-algebras in question together with a description of the range of the classifying invariant on (higher-rank) graph algebras. This problem is open, even for purely infinite Cuntz--Krieger algebras; see [*DO PHANTOM CUNTZ-KRIEGER ALGEBRAS EXIST?*](http://arxiv.org/pdf/1210.6515v1)