  How people connect with one another is a fundamental question in the social
sciences, and the resulting social networks can have a profound impact on our
daily lives. Blau offered a powerful explanation: people connect with one
another based on their positions in a social space. Yet a principled measure of
social distance, allowing comparison within and between societies, remains
elusive. We use the connectivity kernel of conditionally-independent edge
models to develop a family of segregation statistics with desirable properties:
they offer an intuitive and universal characteristic scale on social space
(facilitating comparison across datasets and societies), are applicable to
multivariate and mixed node attributes, and capture segregation at the level of
individuals, pairs of individuals, and society as a whole. We show that the
segregation statistics can induce a metric on Blau space (a space spanned by
the attributes of the members of society) and provide maps of two societies.
Under a Bayesian paradigm, we infer the parameters of the connectivity kernel
from eleven ego-network datasets collected in four surveys in the United
Kingdom and United States. The importance of different dimensions of Blau space
is similar across time and location, suggesting a macroscopically stable social
fabric. Physical separation and age differences have the most significant
impact on segregation within friendship networks with implications for
intergenerational mixing and isolation in later stages of life.
