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

翻译：功能是一种图复杂度度量，它扩展了多种参数，如顶点度、退化性、团宽度或双宽度。在本文中，我们证明功能性在$\mathbb{R}^1$中的盒相交图（即区间图）上有界，而在$\mathbb{R}^3$中的盒相交图上无界。我们还研究了一个称为对称差的参数，该参数介于双宽度与功能性之间，并证明该参数在区间图和$\mathbb{R}^2$中的单位盒相交图上均无界。