## 2 Results and Discussion
### Pearson's correlation Analysis and HCA
The above analyses demonstrated the complex interactions between nitrogen and carbon metabolism of primary and secondary metabolites, connected via biochemical networks of metabolic pathways. Most amino acids, catechin, and epicatechin levels in cluster 1 were positively correlated with each other; however, they were negatively correlated with the levels of terpenoids and anthocyanins in clusters 3 and 4, such as tocopherols, carotenoids, phytosterols, peonidin-3-glucose, and cyanidin-3-glucose. In addition, the levels of terpenoids and anthocyanins in clusters 3 and 4 were positively correlated. These observations were in agreement with the findings of a previous study reporting that carotenoids and flavonoids are positively correlated [3]. However, in the present study, correlations of the levels of not only carotenoids, but also of terpenoids, such as monoterpenes, phytosterols, and tocopherols, with the levels of flavonoids were determined. The metabolite with the highest correlation coefficient for anthocyanins was \(\beta\)-carotene (peonidin-3-\(O\)-glucose, \(r=0.7162\), \(p<0.0001\); cyanidin-3-\(O\)-glucose, \(r=0.7481\), \(p<0.0001\)) (Table 88). In addition, monoterpenes, such as D-limonene, \(p\)-cymene, \(\alpha\)-pinene, linalool, and \(\gamma\)-terpinene, showed positive correlation coefficient values. Among monoterpenes, D-limonene (peonidin-3-\(O\)-glucose, \(r=0.5655\), \(p<0.0001\); cyanidin-3-\(O\)-glucose, \(0.6052\), \(p<0.0001\)) and \(p\)-cymene (peonidin-3-\(O\)-glucose, \(r=0.4633\), \(p=0.0005\); cyanidin-3-\(O\)-glucose, \(r=0.4857\), \(p=0.0005\)) showed high correlation coefficient values and were closely clustered with anthocyanins. The highest correlation coefficient between triterpen and flavonoids was for stigmasterrol (peonidin-3-\(O\)-glucose, \(r=0.4343\), \(p=0.002\); cyanidin-3-\(O\)-glucose, \(r=0.4412\), \(p=0.0017\)) and campesterol (peonidin-3-\(O\)-glucose, \(r=0.4226\), \(p=0.0028\); cyanidin-3-\(O\)-glucose, \(r=0.4530\), \(p=0.0012\)). Furthermore, the most significant positive correlation between tetraterpenes and flavonoids was for lutein (peonidin-3-\(O\)-glucose, \(r=0.4245\), \(p=0.0026\); cyanidin-3-\(O\)-glucose, \(r=0.4409\), \(p=0.0017\)) and \(\alpha\)-tocopherol (peonidin-3-\(O\)-glucose, \(r=0.3198\), \(p=0.0267\); cyanidin-3-\(O\)-glucose, \(r=0.3408\), \(p=0.0178\)), except for \(\beta\)-carotene (the highest correlation value). According to these correlations between terpenoids and anthocyanins, the BR cultivars showed abundance of terpenoids in proportion to the concentrations of anthocyanins (Tables S9 and S10). The BR cultivars in order of pigment (anthocyanions) concentration were as follows: SW 505 (cyanidin-3-\(O\)-glucose, \(742.65\pm 15.69\) ug/g; peonidin-3-\(O\)-glucose, \(32.65\pm 0.73\) ug/g), HJJ (cyanidin-3-\(O\)-glucose, \(493.23\pm 30.50\) ug/g; peonidin-3-\(O\)-glucose, \(20.73\pm 0.53\) ug/g), and JSHC (cyanidin-3-\(O\)-glucose, \(267.27\pm 13.27\) ug/g; peonidin-3-\(O\)-glucose, \(14.06\pm 1.46\) ug/g) (Table S10). These three BR cultivars showed 2-5-times higher concentrations of monoterpenes as well as of triterpenenes and tetraterpenes compared with the respective concentrations in other rice cultivars. On the contrary, the concentrations of catechin and epicatechin showed negative correlation coefficients (\(r=-0.5040\) to \(0.0090\)) with those of terpenoids (Table S8). In cluster 2, fatty acids concentrations were negatively correlated with the levels of flavonoids, such as catechin, epicatechin, peonidin-3-glucose, and cyanidin-3-glucose. Furthermore, in cluster 3, protocatechin acid (peonidin-3-\(O\)-glucose, \(r=0.6936\), \(p<0.0001\); cyanidin-3-\(O\)-glucose, \(r=0.6654\), \(p<0.0001\)) and vanillic acid (peonidin-3-\(O\)-glucose, \(r=0.6860\), \(p<0.0001\); cyanidin-3-\(O\)-glucose, \(r=0.6079\), \(p<0.0001\)) concentrations were positively correlated with those of anthocyanins.