A coarse graining algorithm based on m-order degree in complex network

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. (C) 2020 Elsevier B.V. All rights reserved.