An approach for module identification, Modules of Networks (MoNet), introduced an intuitive module definition and clear detection method using edges ranked by the Girvan-Newman algorithm. Modules from a yeast network showed significant association with biological processes, indicating the method's utility; however, systematic bias leads to varied results across trials. MoNet modules also exclude some network regions. To address these shortcomings, we developed a deterministic version of the Girvan-Newman algorithm and a new agglomerative algorithm, Deterministic Modularization of Networks (dMoNet). dMoNet simultaneously processes structurally equivalent edges while preserving intuitive foundations of the MoNet algorithm and generates modules with full network coverage.