  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.
