| 具有双峰特性的双层超网络模型 |
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| 引用本文： | 卢文,赵海兴,孟磊,胡枫.具有双峰特性的双层超网络模型[J].物理学报,2021(1):378-386. |
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| 作者姓名： | 卢文 赵海兴 孟磊 胡枫 |
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| 作者单位： | 陕西师范大学计算机科学学院;青海师范大学计算机学院;青海省藏文信息处理与机器翻译重点实验室;藏文信息处理教育部重点实验室 |
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| 基金项目： | 国家自然科学基金(批准号:11661069,61663041);青海省科技计划项目(批准号:2018-ZJ-777);教育部春晖项目(批准号:Z2016101)资助的课题. |
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| 摘 要： | 随着社会经济的快速发展,社会成员及群体之间的关系呈现出了更复杂、更多元化的特点.超网络作为一种描述复杂多元关系的网络,已在不同领域中得到了广泛的应用.服从泊松度分布的随机网络是研究复杂网络的开创性模型之一,而在现有的超网络研究中,基于ER随机图的超网络模型尚属空白.本文首先在基于超图的超网络结构中引入ER随机图理论,提出了一种ER随机超网络模型,对超网络中的节点超度分布进行了理论分析,并通过计算机仿真了在不同超边连接概率条件下的节点超度分布情况,结果表明节点超度分布服从泊松分布,符合随机网络特征并且与理论推导相一致.进一步,为更准确有效地描述现实生活中的多层、异质关系,本文构建了节点超度分布具有双峰特性,层间采用随机方式连接,层内分别为ER-ER,BA-BA和BA-ER三种不同类型的双层超网络模型,理论分析得到了三种双层超网络节点超度分布的解析表达式,三种双层超网络在仿真实验中的节点超度分布均具有双峰特性.
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| 关 键 词： | 超图 ER 随机超网络 双峰特性 双层超网络 |
Double-layer hypernetwork model with bimodal peak characteristics |
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| Lu Wen,Zhao Hai-Xing,Meng Lei,Hu Feng.Double-layer hypernetwork model with bimodal peak characteristics[J].Acta Physica Sinica,2021(1):378-386. |
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| Authors: | Lu Wen Zhao Hai-Xing Meng Lei Hu Feng |
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| Affiliation: | (School of Computer Science,Shaanxi Normal University,Xi’an 710119,China;College of Computer,Qinghai Normal University,Xining 810008,China;Key Laboratory of Tibetan Information Processing and Machine Translation of Qinghai Province,Xining 810008,China;Key Laboratory of Tibetan Information Processing,Ministry of Education,Xining 810008,China) |
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| Abstract: | With the rapid development of social economy,the relationship between social members and groups has shown more complex and diverse characteristics.As a network depicting complex relation and multi-layer,hyper network has been widely used in different fields.Random network that obeys Poisson distribution is one of the pioneering models studying complex networks.In the existing hyper network researches,the hyper network based on ER random graph is still a blank.In this paper,we first propose an ER random hyper network model which is based on the hypergraph structure and it adopts the ER random graph theory.Furthermore,using this model,the node hyper degree distribution of this hyper network model is analyzed theoretically,and the node hyper degree distribution is simulated under different hyper edge probabilities:p=0.004 p=0.006 p=0.008 and p=0.01.The results show that the node hyper degree distribution of this hyper network model complies to the Poisson distribution p(k)≈<λ>^k/k!e^-<λ>,which conforms with the characteristics of random networks and is consistent with the theoretical derivation.Further,in order to more accurately and effectively describe the multiple heterogeneous relationship in real life,in this paper we construct three different kinds of double-layer hyper network models with node hyper degree distribution with bimodal peak characteristics.The three kinds respectively are ER-ER,BA-BA and BA-ER,where ER represents the ER random hyper network,and BA denotes the scale-free hyper network,and the layers are connected by a random manner.The analytical expressions of node hyper degree distribution of the three kinds of double-layer hyper network models are obtained by theoretical analysis,and the average node hyper degrees of the three doublelayer hyper networks are closely related to the inter-layer hyper edge probability.As the inter-layer hyper edge probability increases,the average node hyper degree increases.The results of simulation experiments show that the node hyper degree distributions of three kinds of double-layer hyper network models proposed in this paper possess the characteristics of bimodal peaks.The ER random hyper network model and the double-layer hyper network model proposed in this paper provide the theories for further studying the hyper network entropy,hyper network dynamics,hyper network representation learning,hyper network link prediction,and traffic hyper network optimization of such hyper networks in the future,and also it has certain reference significance for studying the evolution of multilayer hyper networks. |
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| Keywords: | hypergraph ER random hyper network bimodal peaks characteristic double-layer hyper network |
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