Growing Networks with Super-Joiners

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 ${\gamma }_{\mathrm{KR}}=1+1/r$, 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 ${\gamma }_{\mathrm{KR}}(r)$ dictated by the redirection mechanism.

10 pages, 5 figures

References in corpus (4)

• Synchronization in complex networks
• Critical phenomena in complex networks
• The Dynamics of a Mobile Phone Network
• Optimal synchronization of complex networks