Criticality and Popularity in Social Networks

TL;DR

This paper models information sharing in social networks as age-dependent branching processes, characterizing criticality and deriving exact popularity distributions, revealing viral behavior with fat-tailed distributions.

Contribution

It introduces a novel interpretation of social network sharing models as age-dependent branching processes and develops a moment-closure method for analyzing their popularity distributions.

Findings

Models can be interpreted as age-dependent multi-type branching processes.

Developed a moment-closure method to handle high-dimensional models.

Exact popularity distribution shows fat tails with order minus three halves.

Abstract

I find that several models for information sharing in social networks can be interpreted as age-dependent multi-type branching processes, and build them independently following Sewastjanow. This allows to characterize criticality in (real and random) social networks. For random networks, I develop a moment-closure method that handles the high-dimensionality of these models: By modifying the timing of sharing with followers, all users can be represented by a single representative, while leaving the total progeny unchanged. Thus I compute the exact popularity distribution, revealing a viral character of critical models expressed by fat tails of order minus three half.