A final metric used was the degree product. This is based on the fact that scale-free networks are thought to grow via preferential attachment, where the probability of a vertex connecting to another given vertex is proportional to its degree . Unlike the models to which this theory was first applied the network here is directed. Hence the metric was slightly modified. As Mislove et al. point out, in a directed network preferential attachment subdivides into preferential creation (the probability to create a new link which is proportional to a node's out-degree) and preferential inception (the probability to receive a new link which is proportional to the node's in-degree) . The form used in was modified to yield: