Biological networks having complex connectivity have been widely studied recently. By characterizing their inherent and structural behaviors in a topological perspective, these studies have attempted to discover hidden knowledge in the systems. However, even though various algorithms with graph-theoretical modeling have provided fundamentals in the network analysis, the availability of practical approaches to efficiently handle the complexity has been limited. In this paper, we present a novel flow-based approach, called flowNet, to efficiently analyze large-sized, complex networks. Our approach is based on the functional influence model that quantifies the influence of a biological component on another. We introduce a dynamic flow simulation algorithm to generate a flow pattern which is a unique characteristic for each component. The set of patterns can be used in identifying functional modules (i.e., clustering). The proposed flow simulation algorithm runs very efficiently in sparse networks. Since our approach uses a weighted network as an input, we also discuss supervised and unsupervised weighting schemes for unweighted biological networks. As experimental results in real applications to the yeast protein interaction network, we demonstrate that our approach outperforms previous graph clustering methods with respect to accuracy.