A dynamic process reference model for sparse networks with reciprocity

ABSTRACT

Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built on top of simple Bernoulli baseline (or reference) measures often behave unrealistically in this respect, leading to the development of sparse reference models that preserve features such as mean degree scaling. In this paper, we generalize recent work on the micro-foundations of such reference models to the case of sparse directed graphs with non-vanishing reciprocity, providing a dynamic process interpretation of the emergence of stable macroscopic behavior.

KEYWORDS:

• Exponential family random graph models
• reciprocity
• reference measures
• social networks
• dynamic processes
• contact formation process

Notes

¹ Contrary to what the name implies, networks undergoing “power law densification” are actually growing more sparse. They are, however, doing so more slowly than they would under constant mean degree.

Additional information

Funding

This work was supported by NSF awards SES [1826589], IIS [1939237], and DMS [1361425].