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In many social networks, there is a high correlation between the similarity of actors and the existence of relationships between them. This paper introduces a model of network evolution where actors are assumed to have a small aversion from being connected to others who are dissimilar to themselves, and yet no actor strictly prefers a segregated network. This model is motivated by Schelling’s [Schelling TC (1969) Models of segregation. Am Econ Rev 59:488–493] classic model of residential segregation, and we show that Schelling’s results also apply to the structure of networks; namely, segregated networks always emerge regardless of the level of aversion. In addition, we prove analytically that attribute similarity among connected network actors always reaches a stationary distribution, and this distribution is independent of network topology and the level of aversion bias. This research provides a basis for more …