Many research have found that individuals' interpersonal environments are patterned as clusters of similar people. However, it is often studied using descriptive analysis and mostly at the level of dyads. Moreover, less attention has been paid to the underlaying mechanisms leading to such patterns.

This paper uses Exponential Random Graph Model (ERGM) to study gender homophily in Facebook friendships at the level of personal networks. It studies Facebook friendship formation as a selective process which is limited by structural constraints (propensity to form tie) and transitivity (friend of friend is more likely to become friend).

Since, collecting personal network data apposite to the statistical inferences is costly and biased toward strong ties, captured data by social network sites (SNSs) provides a novel opportunity in research into social network analysis at the ego-centric level . In this paper, we use the data on more than 70000 Facebook friendship ties based on personal networks of 112 Australian seniors (50 years of age and older) which is collected from Facebook. Data includes information about network structure and socio-demographic characteristics of participants and their friends.

Our ERGM analysis indicates that transitivity is the most powerful factor in explaining the patterning of our participants personal networks. Male (alters) are more social than females in forming ties, but women are more transitive in their relationships than males. In addition, gender homophily is positive for female but negative for male alters that means, female alters are more likely to choose the same sex, while men tend to choose the opposite sex as Facebook friends.

Comparison between male and female participants in terms of the factors patterning their interpersonal environment, shows that personal networks of male and female participants are not different in terms of their underlaying mechanisms. This paper will also discuss the advantages and challenges of using Facebook in studying homophily in personal networks, along with some of the methodological considerations in applying ERGM to such networks.

Keywords: gender homophily, ERGM, personal networks, Facebook