Filter networks, i.e. decomposition of a filter set into a layered structure of sparse subfilters has been proven successful for e.g. efficient convolution using finite impulse response filters. The efficiency is due to the significantly reduced number of multiplications and additions per data sample that is required. The computational gain is dependent on the choice of network structure and the graph representation compactly incorporates the network structure in the design objectives. Consequently the graph representation forms a framework for searching the optimal network structure. It also removes the requirement of a layered structure, at the cost of a less compact representation.