This paper analyses the adequacy of different types of networks in biological process modeling. The assumptions are sustained by two case studies. The first one is a lattice-based computer model to simulate the growth of nonvascular tumors with nutrient consumption constraints. The modeling solution is able to reproduce the classic three-layer structure familiar from multicellular spheroids: cell proliferation, quiescent and necrosis. The accuracy of this model is tested by comparing it to a fractal morphometric technique of two patterns, one of them obtained by simulation, the other developed in vitro. The second application is the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. This is a new preferential attachment scheme, different from those specific for the construction of scale-free graphs, because its new nodes prefer to attach to existing nodes with lower degree. We relate this mechanism to a simple food-web model studied by simulations.