By changing the "rewiring probability " slider, it is possible to explore different regimes both in complex network theory and in the eigenvalue spacing distributions known from random matrix theory (RMT). In this way, a relationship between them can be investigated dynamically.

When the rewiring probability is zero or very small (), the network graph is in the regular regime and the histogram of the unfolded eigenvalue nearest-neighbor spacings can be described by a Poisson distribution. In the extreme opposite case, the pure random graph regime, the rewiring probability , and the histogram of the eigenvalue spacings follows the Wigner surmise function from the Gaussian orthogonal ensemble (GOE) statistics. In the intermediate small-world regime (), the eigenvalue spacing distribution can be modeled by a critical semi-Poisson-like function, whose onset occurs at . For intermediate values in the range , the eigenvalue spacing statistics are actually intermediate between the critical and the GOE regime.