EVOLUTION OF A RANDOM NETWORK disconnected nodes NETWORK. <k>=1 (Erdos and Renyi,1959) The fact that at least one link per node is necessary to have a giant component is not unexpected.Indeed,for a giant component to exist,each of its nodes must be linked to at least one other node. It is somewhat unexpected,however that one link is sufficient for the emergence of a giant component. It is equally interesting that the emergence of the giant cluster is not gradual,but follows what physicists call a second order phase transition at <k>=1. <kc>=1 (Erdos and Renyi, 1959) EVOLUTION OF A RANDOM NETWORK disconnected nodes ➔ NETWORK. The fact that at least one link per node is necessary to have a giant component is not unexpected. Indeed, for a giant component to exist, each of its nodes must be linked to at least one other node. It is somewhat unexpected, however that one link is sufficient for the emergence of a giant component. It is equally interesting that the emergence of the giant cluster is not gradual, but follows what physicists call a second order phase transition at <k>=1