A preference for diversity has been identified as an important predictor of tie formation in certain networks, both social and organizational, that also exhibit a high degree of suppleness–the ability to retain their general form and character under stress (Durkheim, 1893⁄1997. The division of labor in society; Powell et al., 1996. Administrative Science Quarterly 116–145; Powell et al., 2005. American Journal of Sociology, 110(4), 1132–1205; Koput & Gutek, 2010. Gender stratification in the IT industry: Sex, status and social capital. Edward Elgar Publishing). Extant models of preferential attachment, based on popularity, similarity, and cohesion, meanwhile, produce exceedingly brittle networks (Albert et al., 2000. Nature, 406(6794), 378–382; Callaway et al., 2000. Physical Review Letters, 85(25), 5468–5471; Holme et al., 2002. Physical Review E, 65(2), 026107; Shore et al., 2013 Social Networks, 35(1), 116–123). A model of preferential attachment based on diversity is introduced and simulated, demonstrating that a preference for diversity can create a structure characterized by suppleness. This occurs because a preference for diversity promotes overlapping and redundant weak ties during the early stages of network formation.