Elucidating the origins of Preferential Attachment
The mechanism of Preferential Attachment (PA) has a long and
illustrious history. First introduced by the mathematician Polya in
the 1920's, it is based on the premise that "the rich get richer" --
i.e., your rate of growth is proportional to your current size. This
mechanism was used by Zipf to explain the observed distribution of city
sizes, and by Simon to explain the observed distribution of wealth in
ecomonies. More recently, Barabasi and Albert used these ideas to
explain the power-law-like degree distributions observed in many
networks, from the Internet to protein interaction networks.
Despite
its extensive use, PA has always been assumed at the axiomatic level.
No one has before provided an explanation for how this mechanism can
arise. In recent work (D'Souza, et al., PNAS 104 (15) 2007)
we show that PA can arise from the optimization of competition between
resources. In addition, or model gives rise to two other mehanisms:
saturation and viability. This work was featured on the cover of PNAS.