What makes a network go round? Exploring the structure of a strong component with exponential random graph models

• We model the social and structural bases of a strong component using ERGM.
• While mutual reachability in strong components suggests parity, we find hierarchy.
• Some nodes are densely interconnected; others are weakly attached to the component.
• Strong components stem from triadic clustering and lack of preferential attachment.
• These structural processes link to multiplicity of social connectivity in Florence.

A strong component is a subgraph in a directed network where, following the direction of ties, all nodes in the graph are reachable from one another. Mutual reachability implies that every node in the graph is theoretically able to send materials to and/or influence every other node suggesting that strong components are amongst the more egalitarian network structures. Despite this intriguing feature, they remain understudied. Using exponential random graph models (ERGM) for directed networks, we investigate the social and structural processes underlying the generation of strong components. We illustrate our argument using a network of 301 nodes and 703 personal lending ties from Renaissance Florence. ERGM shows that our strong component arises from triadic clustering alongside an absence of higher-order star structures. We contend that these processes produce a strong component with a hierarchical, rather than an egalitarian structure: while some nodes are deeply embedded in a dense network of exchange, the involvement of others is more tenuous. More generally, we argue that such tiered core-periphery strong components will predominate in networks where the social context creates conditions for an absence of preferential attachment alongside the presence of localized closure. Although disparate social processes can give rise to hierarchical strong components linked to these two structural mechanisms, in Florence they are associated with the presence of multiple dimensions of social status and the connectedness of participants across disparate network domains.