Abstract: Compared to single-layer networks, multilayer networks exhibit a more complex node degree composition, comprising both intra-layer and inter-layer degrees. However, the distinct impacts of these degree types on cascading failures remain underexplored. Distinguishing their effects is crucial for a deeper understanding of network structure, information propagation, and behavior prediction. This paper proposes a capacity-load model to influence and compare the influence of different degree types on cascading failures in multilayer networks. By designing three node removal strategies based on total degree, intra-layer degree, and inter-layer degree, simulation experiments are conducted on four types of networks. Network robustness is evaluated using the maximum number of removable nodes before collapse. The relationships between network robustness and the coupling coefficient, as well as load and capacity adjustment parameters, are also analyzed. The results indicate that the node removal strategy with the least impact on cascading failures varies across different types of networks, revealing the significance of different node degrees in failure propagation. Compared to other models, the proposed model enables networks to maintain a higher maximum number of removable nodes during cascading failures, demonstrating superior robustness.

Key words: Multilayer network, Robustness, Cascading failure, Capacity load model