Coexistence in preferential attachment networks

TL;DR

This paper introduces a new competitive model on growing networks that combines preferential attachment with evolving node types, revealing conditions under which multiple types coexist in large networks, aligning with real-world observations.

Contribution

The paper extends the preferential attachment model to include evolving node types and analyzes the conditions for coexistence of multiple competitors in large networks.

Findings

Multiple competitors often coexist in the model.

The model's behavior aligns with empirical observations.

The proportion of types stabilizes in large networks.

Abstract

We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses neighbours by preferential attachment, and selects its type based on the number of initial neighbours of each type. The model is analysed in detail, and in particular, we determine the possible proportions of the various types in the limit of large networks. An important qualitative feature we find is that, in contrast to many current theoretical models, often several competitors will coexist. This matches empirical observations in many real-world networks.