In order to measure, predict, and prevent social segregation, it is necessary
to understand the factors that cause it. While in most available descriptions
space plays an essential role, one outstanding question is whether and how this
phenomenon is possible in a well-mixed social network. We define and solve a
simple model of segregation on networks based on discrete convictions. In our
model, space does not play a role, and individuals never change their
conviction, but they may choose to connect socially to other individuals based
on two criteria: sharing the same conviction, and individual popularity
(regardless of conviction). The trade-off between these two moves defines a
parameter, analogous to the "tolerance" parameter in classical models of
spatial segregation. We show numerically and analytically that this parameter
determines a true phase transition (somewhat reminiscent of phase separation in
a binary mixture) between a well-mixed and a segregated state. Additionally,
minority convictions segregate faster and inter-specific aversion alone may
lead to a segregation threshold with similar properties. Together, our results
highlight the general principle that a segregation transition is possible in
absence of spatial degrees of freedom, provided that conviction-based rewiring
occurs on the same time scale of popularity rewirings.Comment: 11 pages, 8 figure
