Is removal of weak connections necessary for graph-theoretical analysis of dense weighted structural connectomes from diffusion MRI?

Recent advances in diffusion MRI tractography permit the generation of dense weighted structural connectomes that offer greater insight into brain organization. However, these efforts are hampered by the lack of consensus on how to extract topological measures from the resulting graphs. Here we evaluate the common practice of removing the graphs' weak connections, which is primarily intended to eliminate spurious connections and emphasize strong connections. Because this processing step requires arbitrary or heuristic-based choices (e.g., setting a threshold level below which connections are removed), and such choices might complicate statistical analysis and inter-study comparisons, in this work we test whether removing weak connections is indeed necessary. To this end, we systematically evaluated the effect of removing weak connections on a range of popular graph-theoretical metrics. Specifically, we investigated if (and at what extent) removal of weak connections introduces a statistically significant difference between two otherwise equal groups of healthy subjects when only applied to one of the groups. Using data from the Human Connectome Project, we found that removal of weak connections had no statistical effect even when removing the weakest ∼70-90% connections. Removing yet a larger extent of weak connections, thus reducing connectivity density even further, did produce a predictably significant effect. However, metric values became sensitive to the exact connectivity density, which has ramifications regarding the stability of the statistical analysis. This pattern persisted whether connections were removed by connection strength threshold or connectivity density, and for connectomes generated using parcellations at different resolutions. Finally, we showed that the same pattern also applies for data from a clinical-grade MRI scanner. In conclusion, our analysis revealed that removing weak connections is not necessary for graph-theoretical analysis of dense weighted connectomes. Because removal of weak connections provides no practical utility to offset the undesirable requirement for arbitrary or heuristic-based choices, we recommend that this step is avoided in future studies.