Recent studies of cellular networks have revealed modular organizations of genes and proteins. For example, in interactome networks, a module refers to a group of interacting proteins that form molecular complexes and/or biochemical pathways and together mediate a biological process. However, it is still poorly understood how biological information is transmitted between different modules. We have developed information flow analysis, a new computational approach that identifies proteins central to the transmission of biological information throughout the network. In the information flow analysis, we represent an interactome network as an electrical circuit, where interactions are modeled as resistors and proteins as interconnecting junctions. Construing the propagation of biological signals as flow of electrical current, our method calculates an information flow score for every protein. Unlike previous metrics of network centrality such as degree or betweenness that only consider topological features, our approach incorporates confidence scores of protein-protein interactions and automatically considers all possible paths in a network when evaluating the importance of each protein. We apply our method to the interactome networks of Saccharomyces cerevisiae and Caenorhabditis elegans. We find that the likelihood of observing lethality and pleiotropy when a protein is eliminated is positively correlated with the proteins information flow score. Even among proteins of low degree or low betweenness, high information scores serve as a strong predictor of loss-of-function lethality or pleiotropy. The correlation between information flow scores and phenotypes supports our hypothesis that the proteins of high information flow reside in central positions in interactome networks. We also show that the ranks of information flow scores are more consistent than that of betweenness when a large amount of noisy data is added to an interactome. Finally, we combine gene expression data with interaction data in C. elegans and construct an interactome network for muscle-specific genes. We find that genes that rank high in terms of information flow in the muscle interactome network but not in the entire network tend to play important roles in muscle function. This framework for studying tissue-specific networks by the information flow model can be applied to other tissues and other organisms as well.