We introduce the notion of integrability of partial difference equations in two independent variables and how it is related to a consistency relation of maps of a specific type. As a prototypical example, we present the quations that describe non-relativistic elastic collision of two particles in one dimension. Extending these quations to an arbitrary associative algebra, relativistic elastic collision equations turn out to be a particular case. Furthermore, we show that these equations can be reinterpreted as difference systems defined on the Z^2 graph. Finally, if time permits, we will show how this reinterpretation relates the linear and the non-linear approach of discrete analytic functions.