Propinquity drives the emergence of network structure and density
Significance While many studies have focused on how new nodes make connections as they enter a network, we instead consider how choices of additional neighbors, after initial introduction, can shape patterns in emergent network structure. We find the footprints of this type of emergence in real-world networks and discuss how one could estimate the processes driving topology by examination of static snapshots of networks through the lens of link density. Our approach yields insight into network formation in applications ranging from social behavior to drug discovery. The lack of large-scale, continuously evolving empirical data usually limits the study of networks to the analysis of snapshots in time. This approach has been used for verification of network evolution mechanisms, such as preferential attachment. However, these studies are mostly restricted to the analysis of the first links established by a new node in the network and typically ignore connections made after each node’s initial introduction. Here, we show that the subsequent actions of individuals, such as their second network link, are not random and can be decoupled from the mechanism behind the first network link. We show that this feature has strong influence on the network topology. Moreover, snapshots in time can now provide information on the mechanism used to establish the second connection. We interpret these empirical results by introducing the “propinquity model,” in which we control and vary the distance of the second link established by a new node and find that this can lead to networks with tunable density scaling, as found in real networks. Our work shows that sociologically meaningful mechanisms are influencing network evolution and provides indications of the importance of measuring the distance between successive connections.