  Genes have specific functional roles, however, since they are dependent on
each other, they can play a structural role within a network structure of their
interactions. In this study, we analyze the structure of the gene interaction
network and detect the most contributing genes through the random matrix
theory. Specifically, we compare the interaction network of essential and
nonessential genes of the yeast Saccharomyces cerevisiae. Most remarkably, this
well-established combined framework by measuring the node participation ratio
$(NPR)$ index helps detect important genes, which control the insightful
structural patterns in the underlying networks. Results indicate that the
essential genes have higher values of $NPR$ rather than the nonessential ones
which means that they have the most contribution to the network structure. It
is worth mentioning that among all essential genes, the $NPR$ value of 5
significant ones is considerably higher than the other essential genes, and
also the same is for 15 significant nonessential genes compared to the others.
Thus, the significant essential genes strongly manage their network structure,
while the significant nonessential genes, besides their global contributions,
have weak effects on their network structure. Most strikingly, these genes
existing in a limited number of structural patterns are responsible for the
specific bioprocesses which are the signature of their networks.
