Growth model for complex networks with hierarchical and modular structures.
Growth model for complex networks with hierarchical and modular structures.
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DOI：
10.1103/physreve.73.036105
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发表时间：
2006-03
期刊：
影响因子：
--
通讯作者：
Qi Xuan;Yanjun Li;Tie-Jun Wu
中科院分区：
文献类型：
--
作者：
Qi Xuan;Yanjun Li;Tie-Jun Wu
通过在Motter的建模过程中加入沿着增长规则和优先附着规则，提出了一种层次化模块化的网络模型。所提出的模型具有越来越多的顶点，但固定数量的模块和层次结构。顶点形成最低层模块，最低层模块又分层地构成较高层模块。在单个模块或同一级别的两个不同模块中的两个顶点之间创建连接遵循PA规则。该模型的结构特性进行了研究分析和数值。结果表明，该模型的度分布、模块大小分布和聚类函数具有幂律性质，这与许多现实世界中的网络相似。然后，该模型被用来预测现实世界中的模块化和层次结构的网络的增长趋势。通过将该模型与现实网络进行比较，发现了一个有趣的结论：现实世界中的许多网络都处于发展的早期阶段，当增长时间足够大时，网络的模块和级别最终会合并。
A hierarchical and modular network model is suggested by adding a growth rule along with the preferential attachment (PA) rule into Motter's modeling procedure. The proposed model has an increasing number of vertices but a fixed number of modules and hierarchical levels. The vertices form lowest-level modules which in turn constitute higher-level modules hierarchically. The creation of connections between two vertices in a single module or in two different modules of the same level obeys the PA rule. The structural characteristics of this model are investigated analytically and numerically. The results show that the degree distribution, the module size distribution, and the clustering function of the model possess a power-law property which is similar to that in many real-world networks. The model is then used to predict the growth trends of real-world networks with modular and hierarchical structures. By comparing this model with those real-world networks, an interesting conclusion is found: that many real-world networks are in their early stages of development, and when the growth time is large enough, the modules and levels of the networks will be ultimately merged.