Hysteresis in capillary head and relative permeability relationships with saturation degree is an important phenomenon in granular and porous media. Accounting for hysteresis is essential for accurately predicting flow in multiphase systems in hydrological applications such as groundwater management and soil water dynamics. The observed hysteresis loops reflect complex, history-dependent interactions between fluids and pore structures. This work uses three-dimensional (3D) pore network models to systematically investigate how media properties. We analyze the influence of the pore size distribution, correlation, and connectivity on the combined and decoupled mechanisms causing hysteresis: geometric ink bottle effects, non-wetting fluid trapping, and network-dependent effects arising from complex pore accessibility.</p> <p>By leveraging controlled simulated drainage and imbibition scenarios, namely invasion vs random percolation, bond vs site-governed displacement, and with vs without trapping, we decoupled these mechanisms. The different mechanisms present distinct effects on the hysteretic loops. In particular, trapping primarily affects retention curves at high saturation degrees of the wetting phase (<em>S</em><sub>w</sub>) and dramatically reduces wetting-phase relative permeability (<em>k<sup>W</sup></em><sub>r</sub>). In comparison, the ink-bottle effect, driven by pore geometry, is visible across the entire capillary head (<em>h</em><sub>c</sub>) range. In contrast, network hysteresis effects significantly the shape of the retention curve (<em>S</em><sub>w</sub>(<em>h</em><sub>c</sub>) loops and drives <em>k</em><sub>r</sub>(<em>S</em><sub>w</sub>) hysteresis at low <em>S</em><sub>w</sub>.</p> <p>Furthermore, the impact of these mechanisms is highly dependent on medium structure. Increasing the spread of the pore size distribution enhances non-wetting phase trapping volume while mitigating ink bottle effects. Correlation between pore bodies' and throats' radii strongly increases the impact of trapping on <em>k<sup>W</sup></em><sub>r</sub>. Conversely, increasing connectivity (i.e., higher coordination number) reduces the trapped fluid fraction and generally mitigates ink bottle and network hysteresis effects in retention evaluation. These results provide necessary mechanistic understanding, supporting the inverse interpretation of hysteretic loops to deduce the underlying topological structure of porous media.