Topological properties of ER and AB random graphs and subselected networks of 300 nodes and the complete biological networks. Average indegree versus average directed path length for ER and AB random graphs of 300 nodes and biological networks. Biological networks are the complete E. coli (both networks described  and ) and S. cerevisiae network, indicated by the suffix "-complete". Subnetworks containing 300 nodes were created by both the neighbour- and cluster-addition method, indicated by the suffixes "-neighbor" and "-cluster" respectively. The region of the biological networks is enlarged in the upper right corner of the figure. ER and AB random graphs exhibit a phase transition [28,29]. For low connectivity, often no path exists between several pairs of nodes and many path lengths are therefore infinity. These are not considered for calculating the average path length, which therefore appears small because it is calculated from the few short paths that are present. When increasing the p-value (the probability of having an edge), the paths are increasingly made up of more edges until a point is reached where the graph starts forming one giant network. Adding more edges then increases the density of the graph connections, resulting in a decrease of the average path length. ER: Erdös-Rényi, AB: Albert-Barabási.