Network, or graph theoretical, analyses are a powerful and increasingly utilised tool for studying brain connectomics (1). However, graph metrics are highly sensitive to various parameters and as such are highly unstable (2–4). Large phase transitions in topology can lead to instability and regions of high variance across thresholds (fig. 1) (4,5). A common approach to analysing graph metrics is to compute the area under the curve (AUC) across thresholds, e.g. (6). However, this can dilute inferred effects if true effects only manifest in narrow threshold ranges, which is often the case (4). A more recent development is multi-threshold permutation correction (MTPC) (4), which agnostically identifies limited but sustained effects across different threshold levels. However, this method is computationally expensive. A potentially less costly approach is to compute smoothed AUCs (smAUCs). Theoretically, this will smooth out narrow effects across a wider range of thresholds while also reducing the high variance around phase transitions. However, this approach is yet to be tested.To test and compare the sensitivity of smAUCs with different smoothing kernels with the MTPC method in a virtual patient-control comparison.Connectomes for 248 subjects were constructed with deterministic tractography with the damped Lucy-Richardson algorithm (7) (step size = 1mm, angle threshold = 45°, seed point resolution = 2mm³, length threshold=20–500mm, FOD threshold = 0.05, β =1.77, λ = 0.0019, η = 0.04), from 60 direction HARDI acquisition (cardiac gated, b=1200s/mm², TE=87ms, 60 slices, FoV=230×230mm, acquisition matrix=96×96, 2.4mm³ isotropic resolution). Connectivity was inferred between cortical regions of the automated atlas labelling (AAL) atlas (8), with additional a priori anatomical constraints to eliminate spurious streamlines. The datasets were randomly assigned to a 'healthy' or a 'lesioned' group. In the lesioned group a proportion of inter-hemispheric streamlines were removed from the connection (Gaussian distribution with standard deviation ξ, ranged from 0:0.05:0.3). The larger ξ is, the larger the effect size. Four graph metrics were tested: global efficiency, mean clustering coefficient, mean betweenness and smallworldness. Graph metrics were computed across streamline counts of 0:1:30. smAUCs were computed with Gaussian smoothing kernels with FWHMs of σ = 0, 1, 2, 4, 8, 16 and 32 (fig. 2). Permutation corrected p-values (p_corr) were obtained from 500 randomisations. MTPC was also performed across the same threshold range and the same randomisation indices. The sensitivity of each method was assessed from the minimum value for ξ at which p_corr<0.05.In most cases, the MTPC method was sensitive to smaller ξ than the smAUC method (fig. 3, 4). The only exceptions is mean clustering coefficient where the smAUC with σ=32 was more sensitive. Mean betweeness showed no sensitivity to group effects using smAUC. In most cases, the smoothing kernel made no improvement compared to the standard AUC method, although it does have an effect of increased sensitivity for global efficiency.MTPC provides robust testing of statistical effect on graph metrics, allowing the identification of sustained but restricted effects across thresholds. The smAUC theoretically does the same smoothing localised effect across larger ranges of thresholds but without the computational demands of MTPC. However, smAUC does not prevent dilution of the true effect by regions where true effects are hidden due to high variance and does not provide consistently comparable performance compared to MTPC. smAUC shows comparable performance with Global efficiency. This may be explained by this metric being less susceptible to phase transition effects. This indicates that the effect of phase transitions cannot be effectively overcome with smoothing and a more exhaustive search of the threshold space is still required. These results have implications for statistical connectomic network analyses of neuroimaging data, especially in comparison where effects on network topology are expected to be subtle.