Growing Networks with Super-Joiners

TL;DR

This paper extends the Krapivsky-Redner network growth model by allowing new nodes to connect to multiple existing nodes based on a power-law distribution, analyzing how this affects degree distributions in various network types.

Contribution

It introduces a generalized model incorporating multiple connections per new node with a power-law distribution, exploring its impact on degree distributions and network growth dynamics.

Findings

Degree distributions depend on both the power-law exponent and redirection probability.

The model captures more realistic network growth scenarios like social and citation networks.

Potential tension exists between the connection distribution exponent and the redirection mechanism.

Abstract

We study the Krapivsky-Redner (KR) network growth model but where new nodes can connect to any number of existing nodes, $m$, picked from a power-law distribution $p(m)\sim m^{-\alpha}$. Each of the $m$ new connections is still carried out as in the KR model with probability redirection $r$ (corresponding to degree exponent $\gamma_{\rm KR}=1+1/r$, in the original KR model). The possibility to connect to any number of nodes resembles a more realistic type of growth in several settings, such as social networks, routers networks, and networks of citations. Here we focus on the in-, out-, and total-degree distributions and on the potential tension between the degree exponent $\alpha$, characterizing new connections (outgoing links), and the degree exponent $\gamma_{\rm KR}(r)$ dictated by the redirection mechanism.