We propose a new formulation of multi-task feature selection coupled with multiple network regularizers, and show that the problem can be exactly and efficiently solved by maximum flow algorithms. This method contributes to one of the central topics in data mining: How to exploit structural information in multivariate data analysis, which has numerous applications, such as gene regulatory and social network analysis. On simulated data, we show that the proposed method leads to higher accuracy in discovering causal features by solving multiple tasks simultaneously using networks over features. Moreover, we apply the method to multi-locus association mapping with Arabidopsis thaliana genotypes and flowering time phenotypes, and demonstrate its ability to recover more known phenotype-related genes than other state-of-the-art methods.