  In this paper, we show the evaluation of the spectral radius for node degree
as the basis to analyze the variation in the node degrees during the evolution
of scale-free networks and small-world networks. Spectral radius is the
principal eigenvalue of the adjacency matrix of a network graph and spectral
radius ratio for node degree is the ratio of the spectral radius and the
average node degree. We observe a very high positive correlation between the
spectral radius ratio for node degree and the coefficient of variation of node
degree (ratio of the standard deviation of node degree and average node
degree). We show how the spectral radius ratio for node degree can be used as
the basis to tune the operating parameters of the evolution models for
scale-free networks and small-world networks as well as evaluate the impact of
the number of links added per node introduced during the evolution of a
scale-free network and evaluate the impact of the probability of rewiring
during the evolution of a small-world network from a regular network.
