Real-world social networks often exhibit high levels of clustering, positive degree assortativity, short average path lengths (small-world property) and right-skewed but rarely power law degree distributions. On the other hand homophily, defined as the propensity of similar agents to connect to each other, is one of the most fundamental social processes observed in many human and animal societies. In this paper we examine the extent to which homophily is sufficient to produce the typical structural properties of social networks. To do so, we conduct a simulation study based on the Social Distance Attachment (SDA) model, a particular kind of Random Geometric Graph (RGG), in which nodes are embedded in a social space and connection probabilities depend functionally on distances between nodes. We derive the form of the model from first principles based on existing analytical results and argue that the mathematical construction of RGGs corresponds directly to the homophily principle, so they provide a good model for it. We find that homophily, especially when combined with a random edge rewiring, is sufficient to reproduce many of the characteristic features of social networks. Additionally, we devise a hybrid model combining SDA with the configuration model that allows generating homophilic networks with arbitrary degree sequences and we use it to study interactions of homophily with processes imposing constraints on degree distributions. We show that the effects of homophily on clustering are robust with respect to distribution constraints, while degree assortativity can be highly dependent on the particular kind of enforced degree sequence.

中文翻译：

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嗜好是生成社交网络的过程：社交距离依恋模型的见解

现实世界中的社交网络通常表现出高水平的聚类，正度分类性，较短的平均路径长度（小世界属性）和右偏，但很少有幂律度分布。另一方面，同质被定义为相似媒介相互连接的倾向，是许多人类和动物社会中观察到的最基本的社会过程之一。在本文中，我们研究了同构足以产生社交网络典型结构特性的程度。为此，我们基于社交距离附件（SDA）模型（一种特殊的随机几何图（RGG））进行了仿真研究，其中节点被嵌入社交空间中，连接概率在功能上取决于节点之间的距离。我们基于现有的分析结果从第一原理中得出模型的形式，并认为RGG的数学构造直接对应于同构原理，因此它们为它提供了一个很好的模型。我们发现，同质性，特别是与随机边缘重新布线相结合时，足以重现社交网络的许多特征。此外，我们设计了一种混合模型，该模型将SDA与配置模型结合在一起，该模型允许生成具有任意程度序列的同构网络，并使用它来研究同构体与对程度分布施加约束的过程之间的相互作用。我们证明了同构对聚类​​的影响相对于分布约束是稳健的，