Homophily as a Process Generating Social Networks: Insights from Social Distance Attachment Model

Abstract

Real-world social networks o en 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 su icient 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 su icient 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 e ects 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.

Structural complementarity and similarity: linking relational principles to network motifs

“…Starting from very general geometric arguments we linked two fundamental relational principles of similarity and complementarity to their characteristic network motifs, that is, triangles and quadrangles correspondingly, and formulated a comprehensive quantitative framework for measuring the extent to which they shape relations in networks. While similarity and its connections to homophily, triadic closure and the density of ego-nets are well-known [31,32,50,57], the principle of complementarity has not been studied systematically from the network perspective. Here we showed that it is linked to the abundance of quadrangles (4-cycles) and the presence of locally dense bipartitelike subgraphs.…”

“…Hence, the motivating geometric model for similarity-driven relations posits that nodes are positioned in some metric space and the probability of observing a link between them is a decreasing function of the corresponding distance. Such a generic model can be seen as an instance of the class of Random Geometric Graphs (RGGs) [10,50]. The crux is that this very general formulation is enough to guarantee the abundance of triangles (3-cycles), provided that the link probability function decreases with respect to distance at a high enough rate [32].…”

“…Note that the choice of a (hyper)sphere surface is far from arbitrary as it is a specific instance in the broader class of compact homogeneous and isotropic manifolds, for which it has been shown that it is a proper choice for a latent geometry capable of reproducing jointly sparsity with high clustering, small-world effect and arbitrary degree distributions in similarity-driven networks [10]. In other words, in this setting latent geometry can explain some of the most fundamental structural properties of many real-world networks, in particular social networks [50]. Thus, we argue, it is also a natural first choice for representing relations driven by complementarity, especially that thanks to its structure it seems particularly well-suited for this task (but see Ref.…”

“…It is one of the important insights of network science that the statistical overrepresentation of particular motifs (small subgraphs) is very often informative of the underlying generating processes or functional properties of a given system [41]. In particular, there is a large body of evidence showing that the abundance of triangles (3-cycles) is a structural signature of relations driven by similarity between nodes in some (possibly latent) metric space [9,10,12,32,50].…”

Mechanisms and emergent properties of social structure: the duality of actors and social circles

“…A large body of research has made ubiquitous the mechanisms known as preferential attachment, triadic closure, and homophily, and has associated them respectively with degree heterogeneity, high clustering, and segregation (see the comprehensive review by Rivera, Soderstrom, and Uzzi (1) as well as other recent publications (2)(3)(4)(5)(6)(7)(8)(9)(10). However, a consensus on how these mechanisms function and interweave seems distant.…”