Scaling of weighted spectral distribution in weighted small-world networks**Project supported by the National Natural Science Foundation of China (Grant Nos. 61402485, 61573262, and 61303061).

Abstract

Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution (WSD) have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the WSD in a deterministic weighted scale-free small-world network model and find that the WSD grows sublinearly with increasing network order (i.e., the number of nodes) and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the WSD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.