  We analyze gene co-expression network under the random matrix theory
framework. The nearest neighbor spacing distribution of the adjacency matrix of
this network follows Gaussian orthogonal statistics of random matrix theory
(RMT). Spectral rigidity test follows random matrix prediction for a certain
range, and deviates after wards. Eigenvector analysis of the network using
inverse participation ratio (IPR) suggests that the statistics of bulk of the
eigenvalues of network is consistent with those of the real symmetric random
matrix, whereas few eigenvalues are localized. Based on these IPR calculations,
we can divide eigenvalues in three sets; (A) The non-degenerate part that
follows RMT. (B) The non-degenerate part, at both ends and at intermediate
eigenvalues, which deviate from RMT and expected to contain information about
{\it important nodes} in the network. (C) The degenerate part with $zero$
eigenvalue, which fluctuates around RMT predicted value. We identify nodes
corresponding to the dominant modes of the corresponding eigenvectors and
analyze their structural properties.
