Due to the friendship paradox, the average robustness of the single mutation neighbours (μ_n) of genotypes on a neutral network is larger than the average robustness of the genotypes (μ_g). Random walks on neutral networks have an average degree equal to μ_n and, intuitively, we expect that evolution will not converge on populations whose average degree is considerably lower than this. This paper argues that a population achieving an average robustness higher than μ_n is facilitated by nodes of degree higher than μ_n being mutationally biased towards other nodes of degree higher than μ_n. Thus, we present the hypothesis that, for biologically realistic degree distributions, assortativity allows selection to increase robustness above μ_n. Furthermore, although counterexamples do exist, it is argued that it is highly plausible that in the majority of cases in which selection increases robustness above μ_n, that the neutral network is assortative. These arguments are reinforced by simulations of evolution on randomly generated Erdös-Renyi and power-law networks. Elucidating the role of assortativity provides valuable insight into the mechanisms by which robustness evolves as well as the conditions under which it will do so. Moreover, it demonstrates the large influence that higher-order mutational biases can have on evolutionary dynamics.