Onset of Synchronization in Weighted Complex Networks: the Effect of Weight-Degree Correlation

TL;DR

This paper explores how the correlation between link weights and node degrees affects the synchronization onset in complex networks, revealing contrasting effects in correlated and uncorrelated weighting schemes through numerical simulations.

Contribution

It demonstrates the contrasting roles of weight-degree correlation on synchronization, providing insights into how weight distribution influences network dynamics.

Findings

Synchronization improves with weight distribution parameter in WDC networks.

Synchronization deteriorates with the same parameter in WDU networks.

Gradient network analysis explains the contrasting effects on synchronization.

Abstract

By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and node degree is also important to the network dynamics.