社交网络的迭代局部模型
The Iterated Local Model for Social Networks
摘要：
在线社交网络，如Facebook和Twitter，经常从网络中代理之间的友谊关系的角度进行研究。然而，敌对关系在社交网络的结构和功能中也发挥着重要作用，但往往是隐藏的。社交网络的生成机制是由结构平衡理论预测的，该理论假设三人组的代理人更倾向于传递性，即朋友的朋友更可能是朋友，或者是反传递性，即对手的对手成为朋友。先前提出的迭代局部传递性（ILT）和迭代局部反传递性（ILAT）模型分别将传递性和反传递性作为进化机制。这些模型产生了具有社交网络的许多可观察属性的图，例如低直径、高聚类和致密化。我们提出了一个新的，生成模型，称为迭代本地模型（ILM）的社交网络随着时间的推移合成传递和反传递的三元组。在ILM中，我们给出一个可数无限二进制序列作为输入，该序列决定我们是否应用传递或反传递步骤。由此产生的模型表现出在ILT和ILAT模型中观察到的复杂网络的许多特性。特别是，对于任何输入的二进制序列，我们表明，渐近模型生成的有限图，致密，有界的聚类系数从0，直径最多为3，并表现出不良的谱扩展。对ILM图的诱导子图的色数、控制数、Hamilton性和同构类型进行了深入的分析。
英文摘要：
On-line social networks, such as in Facebook and Twitter, are often studied from the perspective of friendship ties between agents in the network. Adversarial ties, however, also play an important role in the structure and function of social networks, but are often hidden. Underlying generative mechanisms of social networks are predicted by structural balance theory, which postulates that triads of agents, prefer to be transitive, where friends of friends are more likely friends, or anti-transitive, where adversaries of adversaries become friends. The previously proposed Iterated Local Transitivity (ILT) and Iterated Local Anti-Transitivity (ILAT) models incorporated transitivity and anti-transitivity, respectively, as evolutionary mechanisms. These models resulted in graphs with many observable properties of social networks, such as low diameter, high clustering, and densification. We propose a new, generative model, referred to as the Iterated Local Model (ILM) for social networks synthesizing both transitive and anti-transitive triads over time. In ILM, we are given a countably infinite binary sequence as input, and that sequence determines whether we apply a transitive or an anti-transitive step. The resulting model exhibits many properties of complex networks observed in the ILT and ILAT models. In particular, for any input binary sequence, we show that asymptotically the model generates finite graphs that densify, have clustering coefficient bounded away from 0, have diameter at most 3, and exhibit bad spectral expansion. We also give a thorough analysis of the chromatic number, domination number, Hamiltonicity, and isomorphism types of induced subgraphs of ILM graphs.
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