The coarse-grained technology of complex networks is a promising method to analyze large-scale networks. Coarse-grained networks are required to preserve some properties of the original networks. In this paper, we propose an m-order-degree-based coarse graining (MDCG) algorithm to keep some statistical properties and controllability of the original network by merging the nodes with the same or similar m-order degree. Compared with the previous coarse-grained algorithms, the proposed algorithm uses the m-order degree as the classification criterion, which not only requires less network information and smaller computation but also preserves more properties, especially to maintain controllability of the original network. Moreover, the proposed algorithm can control the size of the coarse-grained networks freely. The effectiveness of the proposed method is demonstrated by simulation analysis of some model networks and real networks.

复杂网络的粗粒度技术是一种分析大型网络的有前途的方法。需要粗粒度网络来保留原始网络的某些属性。在本文中，我们提出了一种基于m阶度的粗粒度（MDCG）算法，通过合并具有相同或相似m阶度的节点来保留原始网络的某些统计属性和可控性。与以前的粗粒度算法相比，所提出的算法使用米-阶度作为分类标准，不仅需要较少的网络信息和较少的计算，而且保留更多的属性，尤其是保持原始网络的可控性。此外，所提出的算法可以自由地控制粗粒度网络的大小。通过对一些模型网络和真实网络的仿真分析，证明了该方法的有效性。