Propinquity drives the emergence of network structure and density

TL;DR

This paper investigates how the second connection made by new nodes influences network structure and density, revealing that subsequent links are governed by non-random mechanisms that shape network topology.

Contribution

It introduces the propinquity model, demonstrating how second-link distances affect network density and topology, highlighting sociologically meaningful mechanisms in network evolution.

Findings

Second links are non-random and influence network structure.

Snapshots can reveal mechanisms behind second connections.

Propinquity model produces networks with tunable density scaling.

Abstract

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.