期刊论文

Deng, Weibing(wdeng@mail.ccnu.edu.cn);Li, Wei(liw@mail.ccnu.edu.cn)

英文

Communications in Nonlinear Science and Numerical Simulation

1007-5704

2021

99

105804

10.1016/j.cnsns.2021.105804

We gratefully acknowledge Linyuan Lü, Haijun Zhou, Liping Chi, and Shengfeng Deng, give us fruitful suggestions. Thanks to Yueying Zhu, Longfeng Zhao, and Jiao Gu for offer help on network data. This work was supported in part by National Natural Science Foundation of China (Grant No. 61873104 , 11505071 ), the Programme of Introducing Talents of Discipline to Universities under Grant no. B08033, the Financially supported by self-determined research funds of CCNU from the colleges’ basic research and operation of MOE.

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Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications and usually allow for analyticity. There lacks a quantity, however, to tell the ratio of cycles which determines the extent of network being close to tree networks. Therefore we introduce the term Cycle Nodes Ratio (CNR) to describe the ratio of number of nodes belonging to cycles to the number of total nodes, and provide an algorithm to calculate CNR. CNR is...