Quantifying complex network traffic capacity based on communicability sequence entropy

Ma Jin-Long; Zhang Jun-Feng; Zhang Dong-Wen; Zhang Hong-Bin

doi:10.7498/aps.70.20201300

Abstract

The transmission performance of the network depends to a certain extent on the topology of the network. This article analyzes the traffic dynamics of complex networks from the perspective of structural information, and looks for information structure measurement indicators that affect network traffic capacity. Existing research shows that the communicability sequence entropy of complex networks can effectively quantify the overall structure of the network. Based on this measurement, the difference between networks can be effectively quantified, and the connotation of sequence entropy of communicability can be explained. Communication sequence entropy can effectively quantify the overall structure information of the network. In order to characterize the overall traffic capacity of the network, the communication sequence entropy is introduced into the phenomenon of complex network congestion, the correlation between the network communication sequence entropy and the transmission performance is studied, and the internal mechanism of this correlation is analyzed. Simulations in BA scale-free network model and WS small-world network model show that the communication sequence entropy of the network is closely related to its traffic capacity. As the communication sequence entropy increases, the uniformity of the network topology will increase, and the traffic capacity will increase significantly. The traffic capacity of the network is a monotonically increasing function of the entropy of the communication sequence, and is positively correlated with the entropy of the communication sequence. The communication sequence entropy of the network can effectively evaluate the traffic capacity of the network. This conclusion can provide a theoretical basis for the design of a high traffic capacity network and help provide an effective strategy for the design of the high traffic capacity of the network, which can be optimized by increasing the communication sequence entropy.

Keywords:

Authors and contacts

School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China

Corresponding author: Ma Jin-Long, mzjinlong@163.com

Funds: Project supported by the 2020 Military-Civilian Integration Development Research Project of Hebei Province, China (Grant No. HB20JMRH008), the Humanities and Social Sciences Fund of the Ministry of Education of China (Grant No. 19YJAZH069), the National Natural Science Foundation of China (Grant Nos. 61672206, 61572170), the Science and Technology Support Program of Hebei Province, China (Grant Nos. 18210109D, 20310701D), and the High Level Talent Funding Project of Hebei Province, China (Grant No. A2016002015)

FullText HTML : translate this paragraph

References

[1]	Wu G H, Yang H J, Pan J H 2018 Mod. Phys. Lett. B 9 1850137 Google Scholar
[2]	Kumari S, Singh A 2019 Mod. Phys. Lett. B 1 13 Google Scholar
[3]	Jiang L R, Jin X Y, Xia Y X, Ouyang B, Wu D P, Chen X 2014 Int. J. Distrib. Sens. Netw. 1155 764698 Google Scholar
[4]	Tu H C, Xia Y X, Wu J J, Zhou X 2019 Physica A 9 17
[5]	Bianchin G, Pasqualetti F 2020 IEEE Trans. Intell. Transp. 3013 3024 Google Scholar
[6]	Serok N, Levy O, Havlin S, Blumenfeld-Lieberthal E 2019 EPB: Urban Analytics and City Science 1362 1376 Google Scholar
[7]	Li H J, Wang H, Chen L N 2014 Europhys. Lett. 108 68009 Google Scholar
[8]	Xiang J, Wang Z Z, Li H J, Zhang Y, Li F, Dong L P, Li J M, Guo L J 2017 J. Stat. Mech. Theory Exp. 5 053213 Google Scholar
[9]	Chen G, Kong R, Wang Y X 2020 Physica A 540 123002 Google Scholar
[10]	Barabási A L, Albert R 1999 Science 509 512 Google Scholar
[11]	Watts D J, Strogatz S H 1998 Nature 440 442
[12]	Tan F, Wu J J, Xia Y X, Tse C K 2014 Phys. Rev. E 89 062813 Google Scholar
[13]	杨卓璇, 马源培, 李慧嘉 2020 聊城大学学报 (自然科学版) 12 26 Yang Z X, Ma Y P, Li H J 2020 Journal of Liaocheng University (Social Science Edition) 12 26
[14]	马源培, 杨卓璇, 李慧嘉 2020 聊城大学学报(自然科学版) 26 32 Ma Y P, Yang Z X, Li H J 2020 Journal of Liaocheng University (Social Science Edition) 26 32
[15]	Guimerà R, Díaz-Guilera A, Vega-Redondo F, Cabrales A, Arenas A 2002 Phys. Rev. Lett. 89 248701 Google Scholar
[16]	Zhao L, Lai Y C, Park K, Ye N 2005 Phys. Rev. E 71 026125 Google Scholar
[17]	孙磊, 李荣, 靳聪, 陈孝国 2015 科技导报 86 89 Google Scholar Sun L, Li R, Jin C, Chen X G 2015 Science and Technology Review 86 89 Google Scholar
[18]	Chen Z H, Wu J J, Rong Z H, Tse C K 2018 Physica A 191 201
[19]	Cai J, Wang Y, Liu Y, Luo J Z, Wei W G, Xu X P 2018 Future Gener. Comp. Syst. 765 771 Google Scholar
[20]	蔡君, 余顺争 2013 62 058901 Google Scholar Cai J, Yu S Z 2013 Acta Phys. Sin. 62 058901 Google Scholar
[21]	Chen R B, Cui W, Pu C L, Li J, Ji B, Gakis K, Pardalos P M 2018 Physica A 524 532 Google Scholar
[22]	Cui J B, Xiang J, Liu Y, Hu K, Tang Y 2020 J. Phys. Soc. Jpn. 89 014802 Google Scholar
[23]	DuBois T, Eubank S, Srinivasan A 2012 Electron. J. Comb. 1 19
[24]	Hu K, Liu C, Hu T, Tang Y 2010 J. Phys. A: Math. Theor. 43 175101 Google Scholar
[25]	Huang W, Tommy W S C 2010 J. Stat. Mech. Theory Exp. 1 12 Google Scholar
[26]	Jiang Z Y, Liang M G, Guo D C 2011 Int. J. Mod. Phys. C 1211 1226 Google Scholar
[27]	Jiang Z Y, Liang M G, An W J 2014 Physica A 379 385 Google Scholar
[28]	Jiang Z Y, Liang M G, Guo D C 2013 Mod. Phys. Lett. B 8 1350056 Google Scholar
[29]	陈乐瑞, 潘秋萍, 孔金生 2016 计算机系统应用 145 148 Google Scholar Chen L R, Pan Q P, Kong J S 2016 Computer Systems and Applications 145 148 Google Scholar
[30]	孙中悦, 贾兴华 2017 计算机工程 75 78 Google Scholar Sun Z Y, Jia X H 2017 Computer Engineering 75 78 Google Scholar
[31]	Wang D, Liu E W, Liu D, Qu X Y, Ma R F, Wang P, Liu X C 2015 IEEE Commun. Lett. 2110 2113 Google Scholar
[32]	Zhang G Q, Wang D, Li G J 2007 Phys. Rev. E 76 017101 Google Scholar
[33]	Zhang S, Liang M G, Jiang Z Y, Wu J J 2014 Int. J. Mod. Phys. C 6 1450014 Google Scholar
[34]	Zhang Z H, Liu S Y, Yang Y Q, Bai Y G 2019 Cluster Comput. 7687 7694
[35]	申弢, 黄树红, 韩守木, 杨叔子 2001 机械工程学报 94 98 Shen T, Huang S H, Han S M, Yang S Z 2001 Journal of Mechanical Engineering 94 98
[36]	赵荣珍, 张优云 2004 振动、测试与诊断 180 187 Zhao R Z, Zhang Y Y 2004 Journal of Vibration, Measurement and Diagnosis 180 187
[37]	王治忠, 钱龙龙, 韩闯, 师丽 2020 计算机应用 608 615 Google Scholar Wang Z Z, Qian L L, Han C, Shi L 2020 Journal of Computer Applications 608 615 Google Scholar
[38]	Wang B, Tang H W, Guo C H, Xiu Z L 2006 Physica A 363 591 Google Scholar
[39]	吴俊, 谭跃进, 邓宏钟, 朱大智 2007 系统工程理论与实践 101 105 Wu J, Tan Y J, Deng H Z, Zhu D Z 2007 Syst. Engin. Theo. Prac. 101 105
[40]	蔡萌, 杜海峰, 任义科, 费尔德曼 2011 60 110513 Google Scholar Cai M, Du H F, Ren Y K, Marcus W F 2011 Acta Phys. Sin. 60 110513 Google Scholar
[41]	蔡萌, 杜海峰, 费尔德曼 2014 63 060504 Google Scholar Cai M, Du H F, Marcus W F 2014 Acta Phys. Sin. 63 060504 Google Scholar
[42]	胡钢, 徐翔, 高浩, 过秀成 2020 系统工程理论与实践 714 725 Google Scholar Hu G, Xu X, Gao H, Guo X C 2020 Syst. Engin. Theo. Prac. 714 725 Google Scholar
[43]	Chen D, Shi D D, Qin M, Xu S M, Pan G J 2018 Phys. Rev. E 98 012319 Google Scholar
[44]	陈单, 石丹丹, 潘贵军 2019 物理学报 68 118901 Google Scholar Chen D, Shi D D, Pan G J 2019 Acta Phys. Sin. 68 118901 Google Scholar
[45]	石丹丹, 陈单, 龙慧敏, 王承科, 潘贵军 2019 中国科学:物理学力学天文学 49 070502 Google Scholar Shi D D, Chen D, Long H M, Wang C K, Pan G J 2019 Science China Physics, Mechanics and Astronomy 49 070502 Google Scholar
[46]	Estrada E, Hatano N 2008 Phys. Rev. E 77 036111 Google Scholar
[47]	Estrada E 2012 Linear Algebra Appl. 4317 4328 Google Scholar
[48]	Estrada E, Hatano N, Benzi M 2012 Phys. Rep. 89 119 Google Scholar
[49]	Mukherjee G, Manna S S 2005 Phys. Rev. E 71 066108 Google Scholar
[50]	Zhou T, Yan G, Wang B H, Fu Z Q, Hu B, Zhu C P, Wang W X 2006 Dyam. Cont. Dis. Ser. B 13 463
[51]	Barthélemy M 2004 EurPhys. J. B 163 168 Google Scholar
[52]	Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 066109 Google Scholar
[53]	Jiang Z Y, Liang M G 2012 Mod. Phys. Lett. B 29 1250195 Google Scholar
[54]	Yan G, Zhou T, Hu B, Fu Z Q, Wang B H 2006 Phys. Rev. E 73 046108 Google Scholar

Cited By

图 1 网络的通信序列熵S_N与网络的度分布P(k)之间的关系图　(a) BA无标度网络; (b) WS小世界网络

Figure 1. Rrelationship between the network’s communication sequence entropy S_N and the network’s degree distribution P(k): (a) BA scale-free network; (b) WS small world network.

DownLoad: Full-Size Img PowerPoint

图 2 (a)不同的通信序列熵的BA无标度网络下, 有序参数H(R)与数据包生成率R的关系; (b) BA无标度网络通信序列熵$S_{\rm N}$与传输容量$R_{\rm c}$的关系. 采用的路由策略为有效路由策略

Figure 2. (a) Relationship between the order parameter H(R) and the packet generation rate R under BA scale-free network with different communication sequence entropy; (b) relationship between BA scale-free network communication sequence entropy$S_{\rm N}$ and traffic capacity $R_{\rm c}$. The routing strategy adopted is an effective routing strategy.

DownLoad: Full-Size Img PowerPoint

图 3 (a)不同的通信序列熵的WS小世界网络下, 有序参数H(R)与数据包生成率R的关系; (b) WS小世界网络通信序列熵$S_{\rm N}$与传输容量$R_{\rm c}$的关系. 采用的路由策略为有效路由策略

Figure 3. (a) Relationship between the order parameters $H(R)$and the packet generation rate R under the WS small world network with different communication sequence entropy; (b) relationship between WS small world network communication sequence entropy$S_{\rm N}$ and traffic capacity $R_{\rm c}$. The routing strategy adopted is an effective routing strategy.

DownLoad: Full-Size Img PowerPoint

图 4 数据包负载 (traffic load) 在网络中节点度值上的分布情况　(a) BA无标度网络; (b) WS小世界网络

Figure 4. Distribution of traffic load on degree value of nodes in the network: (a) BA scale-free network; (b) WS small world network.

DownLoad: Full-Size Img PowerPoint

图 5 网络的通信序列熵$S_{\rm N}$与平均路径长度$\left\langle {L} \right\rangle $的关系　(a) BA无标度网络; (b) WS小世界网络

Figure 5. Relationship between communication sequence entropy S_N and average path length$\left\langle {L} \right\rangle $ in the network: (a) BA scale-free network; (b) WS small world network.

DownLoad: Full-Size Img PowerPoint

图 6 网络的通信序列熵$S_{\rm N}$与节点的最大介数$B_{\rm {max}}$的关系　(a) BA无标度网络; (b) WS小世界网络

Figure 6. Relationship between communication sequence entropy $S_{\rm N}$ and the maximum betweenness of nodes $B_{\rm {max}}$ in the network: (a) BA scale-free network; (b) WS small world network.

DownLoad: Full-Size Img PowerPoint

map

[1]	Wu G H, Yang H J, Pan J H 2018 Mod. Phys. Lett. B 9 1850137 Google Scholar
[2]	Kumari S, Singh A 2019 Mod. Phys. Lett. B 1 13 Google Scholar
[3]	Jiang L R, Jin X Y, Xia Y X, Ouyang B, Wu D P, Chen X 2014 Int. J. Distrib. Sens. Netw. 1155 764698 Google Scholar
[4]	Tu H C, Xia Y X, Wu J J, Zhou X 2019 Physica A 9 17
[5]	Bianchin G, Pasqualetti F 2020 IEEE Trans. Intell. Transp. 3013 3024 Google Scholar
[6]	Serok N, Levy O, Havlin S, Blumenfeld-Lieberthal E 2019 EPB: Urban Analytics and City Science 1362 1376 Google Scholar
[7]	Li H J, Wang H, Chen L N 2014 Europhys. Lett. 108 68009 Google Scholar
[8]	Xiang J, Wang Z Z, Li H J, Zhang Y, Li F, Dong L P, Li J M, Guo L J 2017 J. Stat. Mech. Theory Exp. 5 053213 Google Scholar
[9]	Chen G, Kong R, Wang Y X 2020 Physica A 540 123002 Google Scholar
[10]	Barabási A L, Albert R 1999 Science 509 512 Google Scholar
[11]	Watts D J, Strogatz S H 1998 Nature 440 442
[12]	Tan F, Wu J J, Xia Y X, Tse C K 2014 Phys. Rev. E 89 062813 Google Scholar
[13]	杨卓璇, 马源培, 李慧嘉 2020 聊城大学学报 (自然科学版) 12 26 Yang Z X, Ma Y P, Li H J 2020 Journal of Liaocheng University (Social Science Edition) 12 26
[14]	马源培, 杨卓璇, 李慧嘉 2020 聊城大学学报(自然科学版) 26 32 Ma Y P, Yang Z X, Li H J 2020 Journal of Liaocheng University (Social Science Edition) 26 32
[15]	Guimerà R, Díaz-Guilera A, Vega-Redondo F, Cabrales A, Arenas A 2002 Phys. Rev. Lett. 89 248701 Google Scholar
[16]	Zhao L, Lai Y C, Park K, Ye N 2005 Phys. Rev. E 71 026125 Google Scholar
[17]	孙磊, 李荣, 靳聪, 陈孝国 2015 科技导报 86 89 Google Scholar Sun L, Li R, Jin C, Chen X G 2015 Science and Technology Review 86 89 Google Scholar
[18]	Chen Z H, Wu J J, Rong Z H, Tse C K 2018 Physica A 191 201
[19]	Cai J, Wang Y, Liu Y, Luo J Z, Wei W G, Xu X P 2018 Future Gener. Comp. Syst. 765 771 Google Scholar
[20]	蔡君, 余顺争 2013 62 058901 Google Scholar Cai J, Yu S Z 2013 Acta Phys. Sin. 62 058901 Google Scholar
[21]	Chen R B, Cui W, Pu C L, Li J, Ji B, Gakis K, Pardalos P M 2018 Physica A 524 532 Google Scholar
[22]	Cui J B, Xiang J, Liu Y, Hu K, Tang Y 2020 J. Phys. Soc. Jpn. 89 014802 Google Scholar
[23]	DuBois T, Eubank S, Srinivasan A 2012 Electron. J. Comb. 1 19
[24]	Hu K, Liu C, Hu T, Tang Y 2010 J. Phys. A: Math. Theor. 43 175101 Google Scholar
[25]	Huang W, Tommy W S C 2010 J. Stat. Mech. Theory Exp. 1 12 Google Scholar
[26]	Jiang Z Y, Liang M G, Guo D C 2011 Int. J. Mod. Phys. C 1211 1226 Google Scholar
[27]	Jiang Z Y, Liang M G, An W J 2014 Physica A 379 385 Google Scholar
[28]	Jiang Z Y, Liang M G, Guo D C 2013 Mod. Phys. Lett. B 8 1350056 Google Scholar
[29]	陈乐瑞, 潘秋萍, 孔金生 2016 计算机系统应用 145 148 Google Scholar Chen L R, Pan Q P, Kong J S 2016 Computer Systems and Applications 145 148 Google Scholar
[30]	孙中悦, 贾兴华 2017 计算机工程 75 78 Google Scholar Sun Z Y, Jia X H 2017 Computer Engineering 75 78 Google Scholar
[31]	Wang D, Liu E W, Liu D, Qu X Y, Ma R F, Wang P, Liu X C 2015 IEEE Commun. Lett. 2110 2113 Google Scholar
[32]	Zhang G Q, Wang D, Li G J 2007 Phys. Rev. E 76 017101 Google Scholar
[33]	Zhang S, Liang M G, Jiang Z Y, Wu J J 2014 Int. J. Mod. Phys. C 6 1450014 Google Scholar
[34]	Zhang Z H, Liu S Y, Yang Y Q, Bai Y G 2019 Cluster Comput. 7687 7694
[35]	申弢, 黄树红, 韩守木, 杨叔子 2001 机械工程学报 94 98 Shen T, Huang S H, Han S M, Yang S Z 2001 Journal of Mechanical Engineering 94 98
[36]	赵荣珍, 张优云 2004 振动、测试与诊断 180 187 Zhao R Z, Zhang Y Y 2004 Journal of Vibration, Measurement and Diagnosis 180 187
[37]	王治忠, 钱龙龙, 韩闯, 师丽 2020 计算机应用 608 615 Google Scholar Wang Z Z, Qian L L, Han C, Shi L 2020 Journal of Computer Applications 608 615 Google Scholar
[38]	Wang B, Tang H W, Guo C H, Xiu Z L 2006 Physica A 363 591 Google Scholar
[39]	吴俊, 谭跃进, 邓宏钟, 朱大智 2007 系统工程理论与实践 101 105 Wu J, Tan Y J, Deng H Z, Zhu D Z 2007 Syst. Engin. Theo. Prac. 101 105
[40]	蔡萌, 杜海峰, 任义科, 费尔德曼 2011 60 110513 Google Scholar Cai M, Du H F, Ren Y K, Marcus W F 2011 Acta Phys. Sin. 60 110513 Google Scholar
[41]	蔡萌, 杜海峰, 费尔德曼 2014 63 060504 Google Scholar Cai M, Du H F, Marcus W F 2014 Acta Phys. Sin. 63 060504 Google Scholar
[42]	胡钢, 徐翔, 高浩, 过秀成 2020 系统工程理论与实践 714 725 Google Scholar Hu G, Xu X, Gao H, Guo X C 2020 Syst. Engin. Theo. Prac. 714 725 Google Scholar
[43]	Chen D, Shi D D, Qin M, Xu S M, Pan G J 2018 Phys. Rev. E 98 012319 Google Scholar
[44]	陈单, 石丹丹, 潘贵军 2019 物理学报 68 118901 Google Scholar Chen D, Shi D D, Pan G J 2019 Acta Phys. Sin. 68 118901 Google Scholar
[45]	石丹丹, 陈单, 龙慧敏, 王承科, 潘贵军 2019 中国科学:物理学力学天文学 49 070502 Google Scholar Shi D D, Chen D, Long H M, Wang C K, Pan G J 2019 Science China Physics, Mechanics and Astronomy 49 070502 Google Scholar
[46]	Estrada E, Hatano N 2008 Phys. Rev. E 77 036111 Google Scholar
[47]	Estrada E 2012 Linear Algebra Appl. 4317 4328 Google Scholar
[48]	Estrada E, Hatano N, Benzi M 2012 Phys. Rep. 89 119 Google Scholar
[49]	Mukherjee G, Manna S S 2005 Phys. Rev. E 71 066108 Google Scholar
[50]	Zhou T, Yan G, Wang B H, Fu Z Q, Hu B, Zhu C P, Wang W X 2006 Dyam. Cont. Dis. Ser. B 13 463
[51]	Barthélemy M 2004 EurPhys. J. B 163 168 Google Scholar
[52]	Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 066109 Google Scholar
[53]	Jiang Z Y, Liang M G 2012 Mod. Phys. Lett. B 29 1250195 Google Scholar
[54]	Yan G, Zhou T, Hu B, Fu Z Q, Wang B H 2006 Phys. Rev. E 73 046108 Google Scholar

[1]	Wang Ting-Ting, Liang Zong-Wen, Zhang Ruo-Xi. Importance evaluation method of complex network nodes based on information entropy and iteration factor. Acta Physica Sinica, 2023, 72(4): 048901. doi: 10.7498/aps.72.20221878
[2]	Lin Hong, Xia Yong-Xiang, Jiang Lu-Rong. Routing in spatial networks based on shortest path length. Acta Physica Sinica, 2022, 71(6): 068901. doi: 10.7498/aps.71.20211621
[3]	Ma Jin-Long, Du Chang-Feng, Sui Wei, Xu Xiang-Yang. Data traffic capability of double-layer network based on coupling strength. Acta Physica Sinica, 2020, 69(18): 188901. doi: 10.7498/aps.69.20200181
[4]	Wang Li-Na, Cheng Yuan-Yuan, Zang Chen-Rui. A symbolized time series network based on seasonal-trend-loess method. Acta Physica Sinica, 2019, 68(23): 238901. doi: 10.7498/aps.68.20190794
[5]	Chen Dan, Shi Dan-Dan, Pan Gui-Jun. Correlation between the electrical transport performance and the communicability sequence entropy in complex networks. Acta Physica Sinica, 2019, 68(11): 118901. doi: 10.7498/aps.68.20190230
[6]	Li Yong-Jun, Yin Chao, Yu Hui, Liu Zun. Link prediction in microblog retweet network based on maximum entropy model. Acta Physica Sinica, 2016, 65(2): 020501. doi: 10.7498/aps.65.020501
[7]	Li Shi-Bao, Lou Lin-Lin, Chen Rui-Xiang, Hong Li. A pervasive optimized algorithm for complex network routing strategy. Acta Physica Sinica, 2014, 63(2): 028901. doi: 10.7498/aps.63.028901
[8]	Liu Wei-Yan, Liu Bin. Congestion control in complex network based on local routing strategy. Acta Physica Sinica, 2014, 63(24): 248901. doi: 10.7498/aps.63.248901
[9]	Cai Jun, Yu Shun-Zheng. An efficient management strategy for enhancing traffic capacity in scale-free networks. Acta Physica Sinica, 2013, 62(5): 058901. doi: 10.7498/aps.62.058901
[10]	Zhou Ting-Ting, Jin Ning-De, Gao Zhong-Ke, Luo Yue-Bin. Limited penetrable visibility graph for establishing complex network from time series. Acta Physica Sinica, 2012, 61(3): 030506. doi: 10.7498/aps.61.030506
[11]	Gao Zhong-Ke, Jin Ning-De, Yang Dan, Zhai Lu-Sheng, Du Meng. Complex networks from multivariate time series for characterizing nonlinear dynamics of two-phase flow patterns. Acta Physica Sinica, 2012, 61(12): 120510. doi: 10.7498/aps.61.120510
[12]	Gao Xiang-Yun, An Hai-Zhong, Fang Wei. Research on fluctuation of bivariate correlation of time series based on complex networks theory. Acta Physica Sinica, 2012, 61(9): 098902. doi: 10.7498/aps.61.098902
[13]	Wang Dan, Jin Xiao-Zheng. On weightd scale-free network model with tunable clustering and congesstion. Acta Physica Sinica, 2012, 61(22): 228901. doi: 10.7498/aps.61.228901
[14]	Liu Gang, Li Yong-Shu. Routing strategy for complex networks based on gravitation field theory. Acta Physica Sinica, 2012, 61(24): 248901. doi: 10.7498/aps.61.248901
[15]	Liu Gang, Li Yong-Shu. Study on the congestion phenomena in complex network based on gravity constraint. Acta Physica Sinica, 2012, 61(10): 108901. doi: 10.7498/aps.61.108901
[16]	Song Yu-Rong, Jiang Guo-Ping. Epidemic-spreading model for networks with different anti-attack abilities of nodes and nonuniform transmission of edges. Acta Physica Sinica, 2010, 59(11): 7546-7551. doi: 10.7498/aps.59.7546
[17]	Song Qing-Song, Feng Zu-Ren, Li Ren-Hou. Multiple clusters echo state network for chaotic time series prediction. Acta Physica Sinica, 2009, 58(7): 5057-5064. doi: 10.7498/aps.58.5057
[18]	Li Tao, Pei Wen-Jiang, Wang Shao-Ping. Optimal traffic routing strategy on scale-free complex networks. Acta Physica Sinica, 2009, 58(9): 5903-5910. doi: 10.7498/aps.58.5903
[19]	Chen Hua-Liang, Liu Zhong-Xin, Chen Zeng-Qiang, Yuan Zhu-Zhi. Research on one weighted routing strategy for complex networks. Acta Physica Sinica, 2009, 58(9): 6068-6073. doi: 10.7498/aps.58.6068
[20]	Wang Dan, Yu Hao, Jing Yuan-Wei, Jiang Nan, Zhang Si-Ying. Study on the congestion in complex network based on traffic awareness algorithm. Acta Physica Sinica, 2009, 58(10): 6802-6808. doi: 10.7498/aps.58.6802

Catalog

Vol. 70, Issue 7 - 2021-04-05

Metrics

Abstract views: 6009
PDF Downloads: 141
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板