Fig. 3

Weighted Gene Co-expression Network Analysis (WGCNA) for CRC. a This plot shows the scale-free topology model fit (R²) versus soft-thresholding power (β). The highest R² is 0.1847 at β = 9, indicating a weak but improving fit to the scale-free topology as β increases. b This plot displays how the mean connectivity decreases with increasing β. At β = 9, the mean connectivity is low, reflecting network sparsification while retaining some structural connections. c Shows a hierarchical clustering dendrogram of metabolites, where branches represent clusters of similar elements based on their co-expression. The height (Y-axis) indicates the dissimilarity between clusters, with smaller heights representing higher similarity. The horizontal bar below the dendrogram represents module assignments. The turquoise color indicates elements grouped into a co-expression module, while grey represents elements that were not assigned to any module due to low correlation or lack of clustering. d This heatmap represents the correlation between module eigengenes and traits (Case and Control, where Case = CRC and Control = Healthy). Each cell contains the correlation coefficient and its p-value with color intensity indicating the correlation’s strength and direction (red for positive, blue for negative). The grey module, containing unassigned elements, shows a very weak positive correlation with CRC (r = 0.016, p = 0.8) and Healthy (r = 0.034, p = 0.6), both of which are statistically insignificant. The turquoise module, containing co-expressed elements, shows a weak positive correlation with CRC (r = 0.055, p = 0.4) and a weak negative correlation with Healthy (r = − 0.075, p = 0.2), neither of which are significant. This suggests no strong relationship between module expression and CRC. e The turquoise nodes in the network visualisation represent metabolites within the turquoise module, characterized by strong co-expression connections. The edges connecting turquoise nodes reflect the strength of co-expression: red edges represent higher strongly co-expression interactions, and blue edges indicate lower co-expression interactions. Metabolites like"Leu,"and"Ile"are central to this cluster, potentially functioning as hub metabolites coordinating module activity