Coarse graining method based on generalized degree in complex network

Coarse graining technology is one of the important methods to study large-scale complex networks currently. Here, we propose a generalized-degree-based coarse graining (GDCG) approach to extract respectively the undirected or directed coarse-grained networks by merging the nodes with same or similar generalized degree. The new approach provides an adjustable generalized degree by parameter p for preserving some significant properties of the initial networks during the coarse-graining processes. Compared with the existing coarse-graining methods, the GDCG method is only based on the generalized degree, which is not only simple and operable, but also keeps some statistical properties and the synchronizability of the original networks. Moreover, the size of the coarse-grained networks can be chosen freely in the proposed method. Finally, extensive numerical simulations demonstrate the effectiveness of our approach. (C) 2018 Elsevier B.V. All rights reserved.