Consensus Analysis of Two Types of Weighted Dumbbell Networks

The consensus of networks is an important branch of complex network science, and its research results can provide the theoretical basis for understanding the dynamic behavior of networks. The network topology has a significant impact on the robustness of network consensus. This article first assigns edge weights based on the classic dumbbell network model and establishes the weighted network model that is suitable for practical applications. Secondly, the specific analytical formulas of the first-order and second-order consistency indicators of the weighted network are derived by combining the theories of network consensus and graph theory. Furthermore, MATLAB software is used to numerically simulate the dependence of the consistency indicators of two types of dumbbell networks on network size and coupling strength. Finally, it is found that the increase in coupling strength leads to the increase in network consensus, and the dumbbell network with fully connected nodes has better robustness of first-order and second-order coherence.