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

Using Spectral Radius Ratio for Node Degree to Analyze the Evolution of Scale Free Networks and Small World Networks