The identification of large numbers of localised transient extreme ultraviolet (EUV) brightenings, on very small spatial scales, in the quiet Sun corona has been one of the key early results from Solar Orbiter. However, there are still a great deal of unknowns about these events. In this work, we aim to better understand EUV brightenings by investigating their spatial distributions. Specifically, we have investigated whether they occur co-spatially with specific line-of-sight (LoS) magnetic field topologies in the photospheric network. We detected the EUV brightenings in this work using an automated algorithm applied to a high-cadence ($3$ s) dataset sampled over $ minutes on $8$ March 2022 by the Extreme Ultraviolet Imager's $17.4$ nm EUV High Resolution Imager ( Data from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager (SDO/HMI) and Atmospheric Imaging Assembly (SDO/AIA) were used to provide context on the LoS magnetic field and for alignment purposes, respectively. We found a total of $5064$ EUV brightenings within this dataset that are directly comparable to events reported previously in the literature. These events occurred within around $0.015$-$0.020$ <!PCT!>\ of pixels for any given frame. We compared eight different thresholds to split the EUV brightenings into four different categories related to the LoS magnetic field. Using our preferred threshold, we found that $627$ EUV brightenings ($12.4$ <!PCT!>) occurred co-spatially with strong bipolar configurations and $967$ EUV brightenings ($19.1$ <!PCT!>) occurred in weak field regions. Fewer than $10$ <!PCT!>\ of EUV brightenings occurred co-spatially with the unipolar LoS magnetic field, no matter what threshold was used. Of the $627$ strong bipolar EUV Brightenings, $54$ were found to occur co-spatially with cancellation, whilst $57$ occurred co-spatially with emergence. EUV brightenings are primarily found to occur co-spatially with the strong LoS magnetic field in the photospheric network. However, they do not predominantly occur co-spatially with (cancelling) bi-poles.