Protein fluxes provide a more refined notion of protein abundance than raw counts alone by considering potential channels based on protein interaction networks. We propose a novel method to estimate protein fluxes in a protein interaction network using a linear programming model based on the framework of flux balance analysis. When we combine this estimate of protein fluxes with a protein-centric network measure, inspired by egocentric network analysis in sociology, we discover that the fluxes of proteins encoded by hypermutated genes in colon cancer have substantially higher alterations in cancer cells than the protein quantities alone. These alterations remain statistically significant under different network perturbations. We conclude that the importance of a change in the quantity of a protein is determined not only by the protein itself, but also by its network neighbors.