  Lagrange functions are localized bases that have many applications in signal
processing and data approximation. Their structure and fast decay make them
excellent tools for constructing approximations. Here, we propose perturbations
of Lagrange functions on graphs that maintain the nice properties of Lagrange
functions while also having the added benefit of being locally supported.
Moreover, their local construction means that they can be computed in parallel,
and they are easily implemented via quasi-interpolation.
