Daniel ben-Avraham - Clarkson University #
Growing Networks with Super-Joiners #
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 with exponent \(\alpha\). Each of the \(m\) new 
connections is still carried out as in the  KR model with redirection
probability \(r\) (corresponding to a degree exponent \(\gamma=1+1/r\), 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 dictated by the 
redirection mechanism.  This tension results in a rich phase diagram,
describing the network's possible outcomes.