In this paper, we show that the spectral radius ratio for node degree could be used to analyze the variationof node degree during the evolution of complex networks. We focus on three commonly studied models ofcomplex networks: random networks, scale-free networks and small-world networks. The spectral radiusratio for node degree is defined as the ratio of the principal (largest) eigenvalue of the adjacency matrix ofa network graph to that of the average node degree. During the evolution of each of the above threecategories of networks (using the appropriate evolution model for each category), we observe the spectralradius ratio for node degree to exhibit high-very high positive correlation (0.75 or above) to that of thecoefficient of variation of node degree (ratio of the standard deviation of node degree and average nodedegree). We show that the spectral radius ratio for node degree could be used as the basis to tune theoperating parameters of the evolution models for each of the three categories of complex networks as wellas analyze the impact of specific operating parameters for each model.
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