  A social network confers benefits and advantages on individuals (and on
groups), the literature refers to these advantages as social capital. This
paper presents a micro-founded mathematical model of the evolution of a social
network and of the social capital of individuals within the network. The
evolution of the network is influenced by the extent to which individuals are
homophilic, structurally opportunistic, socially gregarious and by the
distribution of types in the society. In the analysis, we identify different
kinds of social capital: bonding capital, popularity capital, and bridging
capital. Bonding capital is created by forming a circle of connections,
homophily increases bonding capital because it makes this circle of connections
more homogeneous. Popularity capital leads to preferential attachment:
individuals who become popular tend to become more popular because others are
more likely to link to them. Homophily creates asymmetries in the levels of
popularity attained by different social groups, more gregarious types of agents
are more likely to become popular. However, in homophilic societies,
individuals who belong to less gregarious, less opportunistic, or major types
are likely to be more central in the network and thus acquire a bridging
capital.
