Real-world social networks often exhibit high levels of clustering, positive degree assortativity and short average path lengths (small-world effect). At the same time homophily, defined as a propensity of similar agents to connect to each other, is one of the most fundamental and universal features observed in both human and animal societies. Hence, it is natural to ask to what extent typical structural properties of social networks can be attributed to homophily. In the presentation I will try to give a partial answer to this question based on a simple model of homophily-driven network formation. Next, I will show how it can be combined with the configuration model to study effects of homophily under strict constraints imposed on degree distributions. Obtained results will be used to formulate some rules of thumb that may be useful for assessing the degree to which an observed social network may be shaped by homophily.