Atmospheric water vapor extraction through adsorption to highly porous materials holds promise for its incorporation into broader technologies, including potable water generation. These technologies require breakthroughs in synthesis and design. Here, we demonstrate a composite of zeolite 13X sorbent for high adsorption capacity infiltrated with a light-weight three-dimensional graphene binder, which effectively networks a substrate structure into the sorbent. The composites described maintained fidelity when passing through the pore structure. This was accomplished by the utilization of a sacrificial polymer for safeguarding channel networking during sorbent infiltration of the binder for the extension of substrate networking. The performance measures for adsorbate loadings and thermal flux are evaluated with additional measurements taken for considering compactions of sorbent/substrates. Graphene/Zeolite 13X with preserved channeling demonstrated specific heat flux at 7664 W/kg, while samples without preserved channeling measured 4206 W/kg. A 0.6 g/cm³ compaction resulted in a 412% and a 368% improvement in mass transport while compaction at 1.2 g/cm³ resulted in a 333% and a 290% improvement in mass transport.