The concept of a steepest ascent path generalizes straightforwardly to a graph and so one might also expect basins of attraction to generalize straightforwardly. However, in general, the maxima of f will not lie exactly on the grid G. This means that the set of points on the graph that are best suited to represent a particular maxima family will not all have exactly the same function values and maxima families can only be approximately defined. In the present work, the definition is based upon an expansion around the local maxima of the graph