Analyzing the heterogeneous structure of the genes interaction network through the random matrix theory

There have been massive efforts devoted to understanding the collective behavior of genes. In this regard, a wide range of studies has focused on pairwise interactions. Understanding collective performance beyond pairwise interactions is a great goal in this field of research. In this work, we aim to analyze the structure of genes’ interaction networks through the random matrix theory. We focus on the Pearson Correlation Coefficient network of about 6000 genes of the yeast Saccharomyces cerevisiae. By comparing the spectrum of the eigenvalues of the interaction networks itself with the spectrum of the shuffled ones, we observe clear evidence that unveils the existence of the structure beyond pairwise interactions in the network of genes. Such difference preserves even when the hubs are excluded. In the global network, we identify 140 eigenvectors that have unnormal large eigenvalues. We then derive the spectrum of genes based on the node participation ratio (NPR) index. We again observe noticeable deviation from a random structure. We indicate about 500 genes that have high values of NPR. Compared with the records of the shuffled network, we present clear pieces of evidence that these high values of NPR are a consequence of the structures of the network.