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Barabási’s research group studied the differences between random networks and networks
that could be described using power-function distribution (Barabási 2003). Figure 2.8 shows that
the degree distribution of random networks (the
number of their points having k connections)
forms a bell curve. Such a network is the public
road map of the USA in which towns are points
and roads between them are connections. There
is no town that would have extremely high
number of connections. Neither towns have less
than two connections. Therefore the number of
connections of the points is rather evenly distributed, most points have similar number of connections and there are no densely connected (having
very many connections) points.
The map of flight routes is different (Fig. 2.8).
Here, points represent airports connected by
direct flights. Some large airports (e.g. Chicago,
Los Angeles, Dallas, Atlanta) have a lot of conFig. 2.7 Strong (thick
line) and weak (thin
line) connections among
the members of the
society based on the idea
of Granovetter (1983)
Fig. 2.8 Random (a) and scale-free (b) networks after Barabási (2003)
2.4 Topology of Systems: Network Theory