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Functionality is a graph complexity measure that extends a variety ofparameters, such as vertex degree, degeneracy, clique-width, or twin-width. Inthe present paper, we show that functionality is bounded for box intersectiongraphs in $\mathbb{R}^1$, i.e. for interval graphs, and unbounded for boxintersection graphs in $\mathbb{R}^3$. We also study a parameter known assymmetric difference, which is intermediate between twin-width andfunctionality, and show that this parameter is unbounded both for intervalgraphs and for unit box intersection graphs in $\mathbb{R}^2$.

Functionality of box intersection graphs