  Investigations of topological uniqueness of gene interaction networks in
cancer cells are essential for understanding this disease. Based on the random
matrix theory, we study the distribution of the nearest neighbor level spacings
$P(s)$ of interaction matrices for gene networks in human cancer cells. The
interaction matrices are computed using the Cancer Network Galaxy (TCNG)
database, which is a repository of gene interactions inferred by a Bayesian
network model. 256 NCBI GEO entries regarding gene expressions in human cancer
cells have been selected for the Bayesian network calculations in TCNG. We
observe the Wigner distribution of $P(s)$ when the gene networks are dense
networks that have more than $\sim 38,000$ edges. In the opposite case, when
the networks have smaller numbers of edges, the distribution $P(s)$ becomes the
Poisson distribution. We investigate relevance of $P(s)$ both to the size of
the networks and to edge frequencies that manifest reliance of the inferred
gene interactions.
