摘要
用随机超网络模型去理解一个真实网络的形成机制是不直观的。针对这一问题,提出一种基于节点迭代的确定性超网络模型,利用分形理论和超网络研究方法,解析了平均超度、超度分布、平均距离和直径等拓扑特性,发现此类超网络的超度分布服从指数分布,超网络平均距离和直径与网络规模的对数成比例。给出了一种节点标号方法,并基于此方法推导出了计算超网络拉普拉斯特征值的递推关系式,此关系式可降低计算超网络拉普拉斯特征值的时间复杂度。研究结果表明,利用该文提出的节点迭代法构造的超网络具有小世界特性,这有助于更好地理解真实网络的复杂性和多样性。
Stochastic models are difficult to explain the shaping of complex networks and interaction between nodes in an intuitive way.To solve this problem,a method of node iteration is proposed to constructa deterministic hypernetwork model.By using fractal theory and hypernetwork research methods,the analytical solutions of some structural properties of the hypernetwork model such as mean hyperdegree is obtained,hyperdegree distribution,average shortest path,diameter and so on.The results show that the hyperdegree distribution of the hypernetwork obeys the exponential distribution;The average path length is proportional to the network size.An efficient node labeling method is presented based on this method,the recursive relations of Laplacian eigenvalues are obtained,which effectively reduces the time complexity of computing the eigenvalues.The above analysis shows that are obtained the method of node iteration is feasible for deterministic hypernetwork modeling,and the hypernetwork has small-world characteristics.The results of this paper are helpful to understand the complexity and diversity of real networks.
作者
李发旭
卫良
LI Faxu;WEI Liang(Computer College,Qinghai Normal University,Xining 810008,China;School of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China;The State Key Laboratory of Tibetan Intelligent Information Processing and Application,Qinghai Normal University,Xining 810008,China)
出处
《电子设计工程》
2023年第3期16-21,共6页
Electronic Design Engineering
基金
国家自然科学基金(61663041)
青海省科技计划项目(2018-ZJ-718)。
关键词
超网络
确定性模型
节点标号
拓扑特性
小世界
拉普拉斯谱
hypernetworks
deterministic model
node labeling
topological property
small-world
Lap-lacian spectra
