Network modeling of biological systems is a powerful tool for analysis of high-throughput datasets by computational systems biologists. Integration of networks to form a heterogeneous model requires that each network be as noise-free as possible while still containing relevant biological information. In earlier work, we have shown that the graph theoretic properties of gene correlation networks can be used to highlight and maintain important structures such as high degree nodes, clusters, and critical links between sparse network branches while reducing noise. In this paper, we propose the design of advanced network filters using structurally related graph theoretic properties. While spanning trees and chordal subgraphs provide filters with special advantages, we hypothesize that a hybrid subgraph sampling method will allow for the design of a more effective filter preserving key properties in biological networks. That the proposed approach allows us to optimize a number of parameters associated with the filtering process which in turn improves upon the identification of essential genes in mouse aging networks.