The two different regimes are a direct consequence of the mixing pattern. In assortatively mixed networks, nodes of high degree preferentially connect to each other and form a highly connected core group. Therefore, for low link density, a larger GC size is found than for either disassortatively mixed or random networks. Link density within the GC is higher than in the network as a whole. In contrast, in disassortatively mixed networks at low link density, the links are more dispersed, forming many isolated components of small size (figure 3). As link density increases, the probability that a link with one node in the GC will only connect to another node already in the GC also increases; this is a finite size effect that is exacerbated by assortative mixing since high-degree nodes are relatively few. Thus, at higher link densities, assortatively mixed networks have a smaller GC size compared with disassortatively mixed networks, as in the latter, added links are more likely to result in smaller components being absorbed into the GC (figure 2). 