Measures of closeness to cordiality for graphs

A graph $G$ is cordial if there exists a function $f$ from the vertices of $G$ to $\{0,1\}$ such that the number of vertices labelled $0$ and the number of vertices labelled $1$ differ by at most $1$, and if we assign to each edge $xy$ the label $\mathrm{\mid }f(x)-f(y)\mathrm{\mid }$, the number of edges labelled $0$ and the number of edges labelled $1$ also differ at most by $1$. We introduce two measures of how close a graph is to being cordial, and compute these measures for a variety of classes of graphs.