Bianconi Ginestra, Darst Richard K, Iacovacci Jacopo, Fortunato Santo
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom.
Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P. O. Box 12200, FI-00076, Finland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042806. doi: 10.1103/PhysRevE.90.042806. Epub 2014 Oct 10.
Most of the complex social, technological, and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored small-world and scale-free properties of these networks. Despite the large interest in characterizing the community structures of real networks, not enough attention has been devoted to the detection of universal mechanisms able to spontaneously generate networks with communities. Triadic closure is a natural mechanism to make new connections, especially in social networks. Here we show that models of network growth based on simple triadic closure naturally lead to the emergence of community structure, together with fat-tailed distributions of node degree and high clustering coefficients. Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation. Communities are the more pronounced, the sparser the graph, and disappear for high values of link density and randomness in the attachment procedure. By introducing a fitness-based link attractivity for the nodes, we find a phase transition where communities disappear for high heterogeneity of the fitness distribution, but a different mesoscopic organization of the nodes emerges, with groups of nodes being shared between just a few superhubs, which attract most of the links of the system.
大多数复杂的社会、技术和生物网络都具有显著的社群结构。因此，复杂网络的社群结构必须被视为一种普遍属性，与这些网络中已被广泛研究的小世界和无标度属性一同看待。尽管人们对刻画真实网络的社群结构有着浓厚兴趣，但对于能够自发产生具有社群的网络的普遍机制的探测却关注不足。三元闭包是建立新连接的一种自然机制，尤其在社交网络中。在此我们表明，基于简单三元闭包的网络增长模型自然会导致社群结构的出现，同时伴随着节点度的幂律分布和高聚类系数。社群从链接浓度的初始随机异质性中涌现，随后经历一个增长和分裂的循环。图形越稀疏，社群越显著，而在链接密度和连接过程中的随机性较高时社群会消失。通过为节点引入基于适应性的链接吸引力，我们发现了一个相变，即当适应性分布的异质性较高时社群消失，但会出现一种不同的节点介观组织，其中节点组仅在少数几个超级中心之间共享，这些超级中心吸引了系统的大部分链接。
