Fig. 2: Relationship between multi-omics periphery and core.

a–d Distinction of peripheral and core regions of four omics aspects (O1, O2, O3, and O4). a The violin chart shows the scales of the neighbourhoods (Table 2) across 15 cancers. The average sizes are 942, 691, 1044, and 976, respectively (median: 936, 687, 1046, and 983). b Of these, the scales of the core regions average 31, 11, 26, and 134, respectively (median: 18, 10, 18, and 42). c We show the LCC z-scores of neighbourhoods across 15 cancers. The average sizes are 0.88, −5.67, 4.01, and 1.93, respectively (median: 0.76, −6.37, 4.2, and 2.08). d LCC z-scores of cores shown with average values of 2.53, −0.62, 7.83, and 0.63 (median, 1.09, −1.03, 7.38, and 0.21). e–g Common peripheries and specific cores. Taking READ as an example, four peripheral and four core regions were obtained from different omics aspects. Network proximity: Jaccard coefficient (JAC), Overlap p-value (hypergeometric test), and network distance between any two regions are shown in the heat maps. The overlap between the peripheral region is large (average JAC = 0.048, p-value = 0.01) and the distance is close (\(s_{AB}\) = 0.21), while the core regions are basically non-overlapping (average JAC = 0.017, p-value = 0.25) and far away (\(s_{AB}\) = 1.05). Correspondingly, grey or green violins display the network proximity values among cores or among peripheries. We noticed significant differences between these violin pairs (Mann–Whitney U test p-values, 1.77 × 10⁻⁵, 1.74 × 10⁻⁵, and 3.49 × 10⁻⁵). h The blue violin describes the network distance between the core and peripheral regions of the same omics aspect; the light blue violin collects the network distance between the core and peripheral regions from different omics aspects. There is no significant difference between these two sets (Mann–Whitney U test p-value, 0.5657). i Button-like structure of the omnigenic neighbourhood. The peripheral regions (highlighted in light green) are common, and the core regions (highlighted in four colours) are specific to the four omics aspects. A node is marked with multiple colours, indicating that it is perturbed in multiple omics aspects. The bar chart shows the number of omics aspects in which a peripheral or core gene is perturbed. The results indicate that most core genes (98%) are perturbed in specific omics aspects, and a certain percentage of peripheral genes (21%) and a few core genes (2%) tend to be perturbed in multiple omics aspects. The error bars indicate the 95% confidence intervals.