Coarse-graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve statistical properties as well as the dynamic behaviors of the initial networks. Some methods have been proposed and found effective in undirected networks, while the study on coarse-graining directed networks lacks of consideration. In this paper we proposed a path-based coarse-graining (PCG) method to coarse grain the directed networks. Performing the linear stability analysis of synchronization and numerical simulation of the Kuramoto model on four kinds of directed networks, including tree networks and variants of Barabási-Albert networks, Watts-Strogatz networks, and Erdös-Rényi networks, we find our method can effectively preserve the network synchronizability.
[1]
J. MacQueen.
Some methods for classification and analysis of multivariate observations
,
1967
.
[2]
N. Mavromatos,et al.
LECT NOTES PHYS
,
2002
.
[3]
宁北芳,et al.
疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
,
2005
.
[4]
R. Rosenfeld.
Nature
,
2009,
Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.