  Let $G=(V,E)$ be a graph and $A$ its adjacency matrix. We say that a vertex
$y \in V$ is a function of vertices $x_1, \ldots, x_k \in V$ if there exists a
Boolean function $f$ of $k$ variables such that for any vertex $z \in V - \{y,
x_1, \ldots, x_k\}$, $A(y,z)=f(A(x_1,z),\ldots,A(x_k,z))$. The functionality
$fun(y)$ of vertex $y$ is the minimum $k$ such that $y$ is a function of $k$
vertices. The functionality $fun(G)$ of the graph $G$ is
$\max\limits_H\min\limits_{y\in V(H)}fun(y)$, where the maximum is taken over
all induced subgraphs $H$ of $G$. In the present paper, we show that
functionality generalizes simultaneously several other graph parameters, such
as degeneracy or clique-width, by proving that bounded degeneracy or bounded
clique-width imply bounded functionality. Moreover, we show that this
generalization is proper by revealing classes of graphs of unbounded degeneracy
and clique-width, where functionality is bounded by a constant. This includes
permutation graphs, unit interval graphs and line graphs. We also observe that
bounded functionality implies bounded VC-dimension, i.e. graphs of bounded
VC-dimension extend graphs of bounded functionality, and this extension is also
proper.
