The giant component (GC) is the largest subset of nodes such that any two nodes from this subset can be connected by a series of links. For undirected networks, the GC size represents the upper limit for the potential size of an epidemic. In figure 2 , the structural differences of preferentially mixed networks are demonstrated by the size of the GC as a function of the cut-off parameter K for three different values of the assortativity coefficient r. As the cut-off parameter increases, the number of links in the network increases and the network becomes denser. A K-value exists where the GC size is equal on disassortatively and assortatively mixed networks. Consistent with previous results ( Newman 2002 ( Newman , 2003a , below this value, GC size is larger on assortatively mixed networks and above it, the GC is larger on disassortatively mixed networks, with GC size generally intermediate on random networks.