Abstract
Weights of edges in many complex networks we constructed are quantized values of the real weights. To what extent does the quantization affect the properties of a network? In this work, quantization effects on network properties are investigated based on the spectrum of the corresponding Laplacian. In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated. We supply theoretical analysis on the critical quantization level and the power laws.
Highlights
Weights of edges in many complex networks we constructed are quantized values of the real weights
In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated
Periodic jumping of eigenvalues with peak-value decreasing in a certain power-law relationship is found in many real-world weighted networks
Summary
Weights of edges in many complex networks we constructed are quantized values of the real weights. Quantization effects on network properties are investigated based on the spectrum of the corresponding Laplacian. In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated. Many networks we constructed and investigated in network science studies are based on quantized weights of edges for convenience or due to limitation on measurement. Periodic jumping of eigenvalues with peak-value decreasing in a certain power-law relationship is found in many real-world weighted networks. Theoretical estimations of the critical quantization level and the peak values are obtained. From quantization effects on the degree-preserving and fully randomized networks, that the critical quantization level is determined by the degree distribution
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