TNF and hepatocellular carcinoma: It is important to note that, according to the degree values, total n-6 PUFA (73), n-6/n-3 ratio (50), and intestinal permeability (IP) (52) in the first largest module, serum LPS (45) and LBP (43) and HCC (40) in the second module, serum IL-6 (37) and TNF-α (36) and body weight (34) in the third module, and total PUFA (14) and n-3 PUFA (27) in the fourth module were linked with microbes and metabolites identified as biologically important with microbe–metabolite inter-omic analysis (Supplementary Fig. 5a).