FIGURE 1. Visual illustration of the difference between an exponential and a scale-free network.

From the following article:

Error and attack tolerance of complex networks

Réka Albert, Hawoong Jeong and Albert-László Barabási

Nature 406, 378-382(27 July 2000)



a, The exponential network is homogeneous: most nodes have approximately the same number of links. b, The scale-free network is inhomogeneous: the majority of the nodes have one or two links but a few nodes have a large number of links, guaranteeing that the system is fully connected. Red, the five nodes with the highest number of links; green, their first neighbours. Although in the exponential network only 27% of the nodes are reached by the five most connected nodes, in the scale-free network more than 60% are reached, demonstrating the importance of the connected nodes in the scale-free network Both networks contain 130 nodes and 215 links (left fencekright fence = 3.3). The network visualization was done using the Pajek program for large network analysis: left fence fence.