title: Growing networks with superjoiners.
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)∼m^{-α}. Each of the m new connections is still carried out as in the KR model with probability redirection r (corresponding to degree exponent γ_{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 α, characterizing new connections (outgoing links), and the degree exponent γ_{KR}(r) dictated by the redirection mechanism.
authors.affiliation: Department of Physics, Clarkson University, Potsdam, New York 13699-5820, USA.
authors.forename: Ameerah
authors.initials: A
authors.lastname: Jabr-Hamdan
authors.affiliation: Department of Mathematics & Computer Science, Clarkson University, Potsdam, New York 13699-5815, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Sun
authors.affiliation: Department of Physics, Clarkson University, Potsdam, New York 13699-5820, USA and Department of Mathematics & Computer Science, Clarkson University, Potsdam, New York 13699-5815, USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: Ben-Avraham