A Dynamic Process Reference Model for Sparse Networks with Reciprocity

TL;DR

This paper introduces a dynamic process reference model for sparse directed networks with reciprocity, explaining how stable macroscopic properties emerge in social and other networks as they grow.

Contribution

It generalizes previous models to include reciprocity in sparse directed graphs, offering a dynamic process interpretation of stable network features.

Findings

Provides a dynamic process interpretation for reciprocity in sparse networks

Generalizes existing models to include non-vanishing reciprocity

Explains the emergence of stable macroscopic network features

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.