A Micro-foundation of Social Capital in Evolving Social Networks

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.

💡 Research Summary

The paper develops a micro‑founded mathematical framework for the evolution of a directed social network and the emergence of three distinct forms of social capital—bonding, popularity, and bridging. Agents belong to heterogeneous social types (e.g., occupation, age, ethnicity) and are characterized by four exogenous parameters: (i) type distribution (population share of each group), (ii) homophily index (preference for same‑type contacts), (iii) gregariousness (minimum number of outgoing links an agent seeks), and (iv) structural opportunism (propensity to meet friends‑of‑friends). Network formation proceeds through three stochastic stages—birth, meeting, and linking—where agents have bounded rationality: they only know the agents they encounter and cannot observe the global network.

Bonding capital is defined as the utility derived from an agent’s ego‑network. It depends on the size of the ego‑network and its homogeneity; higher homophily yields larger bonding capital because links are more likely to provide relevant support and information. The authors prove that extreme homophily (index = 1) is a necessary and sufficient condition for maximizing aggregate bonding capital, but it also creates structural holes—gaps between homogeneous clusters that impede information flow.

Popularity capital measures the number of inbound links (indegree) an agent receives. Structural opportunism introduces a preferential‑attachment mechanism: when agents are more likely to connect to friends‑of‑friends, early popular nodes acquire additional links at a super‑linear rate, leading to “the rich get richer.” The analysis shows that in tolerant (low‑homophily) societies, an individual’s age and the collective gregariousness of its type dominate popularity accumulation, whereas homophily generates asymmetries across groups: more gregarious types become disproportionately popular, while the overall type distribution does not affect the speed of popularity growth.

Bridging capital is captured by betweenness centrality, reflecting an agent’s role as a conduit between otherwise disconnected groups. In highly homophilic societies, agents belonging to less gregarious, less opportunistic, or majority types tend to occupy bridging positions because they are more likely to sit on the few inter‑group links that exist. Simulations confirm that such “weak‑tie” brokers acquire high bridging capital, supporting Granovetter’s theory of the strength of weak ties.

Key theoretical results include:

1. Extreme homophily maximizes bonding capital but reduces bridging capital by increasing network diameter and creating structural holes.
2. Structural opportunism (γ > 0) yields a preferential‑attachment dynamic for popularity capital, amplifying early advantages.
3. Gregariousness accelerates ego‑network formation and boosts both popularity and bridging capital for highly sociable types.
4. Type distribution alone does not drive popularity growth, but when combined with heterogeneity in gregariousness it can widen popularity gaps between minority and majority groups.

The paper’s contributions are twofold. First, it provides a unified stochastic model that links individual behavioral traits to macro‑level network outcomes and the distribution of social capital. Second, it offers policy‑relevant insights: reducing excessive homophily or moderating structural opportunism can simultaneously enhance bonding (through diverse ties) and bridging (by closing structural holes), thereby fostering both social support and innovation. The framework is applicable to online platforms (Twitter follow/retweet dynamics, citation networks) and can guide the design of recommendation algorithms, community‑building interventions, and diversity‑enhancing policies.