## 3 Results
### Weighted Co-Expression Network Construction and Key Module Identification  
Co-expression analysis was carried out to construct a co-expression network (Figure 3). Soft-thresholding power in WGCNA was determined for clustering gene expression  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Up-Regulated Genes**} & \multicolumn{4}{c}{**Down-Regulated Genes**} \\ \hline
**Gene** & **logFC** & \(\mathbf{p}\)**-Value** & **Gene** & **logFC** & \(\mathbf{p}\)**-Value** \\ \hline IGLV3-19 & 14.31 & \(7.2\times 10^{-16}\) & IGLV2-14 & \(-14.10\) & \(1\times 10^{-9}\) \\ RPI-298M8.1 & 12.98 & \(1.3\times 10^{-11}\) & IGLV1-44 & \(-10.86\) & \(2\times 10^{-7}\) \\ IGHV3-48 & 12.56 & \(6.5\times 10^{-12}\) & IGHV4-31 & \(-10.75\) & \(2\times 10^{-7}\) \\ RP11-39K24.12 & 12.50 & \(6.6\times 10^{-12}\) & IGLV1-40 & \(-10.25\) & \(2\times 10^{-7}\) \\ ANNA1 & 12.31 & \(1.1\times 10^{-19}\) & IGLV1-47 & \(-9.93\) & \(7\times 10^{-7}\) \\ RP11-39K24.13 & 12.03 & \(1.6\times 10^{-11}\) & IGKV2-28 & \(-9.92\) & \(3\times 10^{-7}\) \\ RPL17P35 & 11.91 & \(2.0\times 10^{-12}\) & AIF1 & \(-9.76\) & \(5\times 10^{-7}\) \\ RN7S13 BP & 11.81 & \(9.6\times 10^{-11}\) & IGLV7-46 & \(-9.68\) & \(1\times 10^{-6}\) \\ RNU1-8P & 11.74 & \(6.4\times 10^{-12}\) & IGKVID-39 & \(-9.32\) & \(4\times 10^{-6}\) \\ OR10G3 & 11.73 & \(1.8\times 10^{-12}\) & SNORAV0G & \(-9.17\) & \(6\times 10^{-7}\) \\ RP11-83M16.2 & 11.62 & \(1.2\times 10^{-10}\) & IGHV3-30 & \(-9.16\) & \(8\times 10^{-6}\) \\ ACO07560.1 & 11.54 & \(2.9\times 10^{-9}\) & RN7S1237P & \(-8.97\) & \(2\times 10^{-4}\) \\ FCGR2A & 11.47 & \(8.7\times 10^{-11}\) & RP11-90023.1 & \(-8.89\) & \(2\times 10^{-4}\) \\ RN7S1231P & 11.46 & \(1.9\times 10^{-10}\) & TRBV5-6 & \(-8.82\) & \(2\times 10^{-4}\) \\ RNU4 ATAC16P & 11.46 & \(1.9\times 10^{-10}\) & RP11-571F15.3 & \(-8.81\) & \(2\times 10^{-5}\) \\ KRT19P2 & 11.42 & \(7.1\times 10^{-11}\) & RP11-613F22.5 & \(-8.79\) & \(5\times 10^{-5}\) \\ BRS3 & 11.33 & \(1.3\times 10^{-11}\) & IKKV1-39 & \(-8.77\) & \(2\times 10^{-4}\) \\ PSMA6F4 & 11.27 & \(8.4\times 10^{-11}\) & IKIVID-54 & \(-8.67\) & \(2\times 10^{-4}\) \\ RP11-64K12.1 & 11.23 & \(3.6\times 10^{-10}\) & IGKV1-5 & \(-8.66\) & \(1\times 10^{-4}\) \\ CYCSP39 & 11.22 & \(3.7\times 10^{-10}\) & RP11-389C8.3 & \(-8.56\) & \(3\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fold change of genes by differentially expressed gene assay. The top-20 most up/down regulated genes by comparing non-metastatic breast cancer with metastatic breast cancer.  
Figure 2: (a) PCA plot of samples showing distribution of each samples. (b) Volcano plot of differentially expressed genes. (c) Heatmap of gene expression in metastatic and non-metastatic samples.  
(Figure 4). We found 2147 genes of genes of most variance genes (MVGs) with similar gene expression patterns. These genes were included in the modules following cluster analysis. Eight modules showing the same gene expression patterns were identified and analyzed, two of which were related to the metastatic stage and the other six modules were related to the non-metastatic stage. We visualized the gene network with a heatmap and meta-modules (Figure 5). Each colored module represents a gene group with similar gene expression patterns, calculated by WGCNA function. We selected the brown module for analysis, which was the most closely associated with the metastatic stage; this module was crucial to evaluating breast cancer metastasis (R = 0.39, \(p\)-value = 1 \(\times\) 10\({}^{-4}\)).  
Figure 4: Determination of soft-thresholding power in WGCNA. (**a**) Analysis of the scale-free fit index for various soft-thresholding powers (\(\beta\)). (**b**) Analysis of the mean connectivity for various soft-thresholding powers. (**b**) Evaluating the scale free topology when \(\beta\) = 9.  
Figure 3: Clustering dendrogram of 94 samples.