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)

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References

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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

[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 物理学报 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
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[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
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[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
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[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
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[47]	Estrada E 2012 Linear Algebra Appl. 4317 4328 Google Scholar
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[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

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