Nonlinear networks have an uneven power law distribution
The distribution of components in nonlinear networks follows an uneven power law distribution. For instance, the Sun is composed of 71 percent hydrogen and 27 percent helium. The remaining two percent is composed of a variety of elements that are not equally distributed. Oxygen is the most abundant of that two percent (at 42.9 percent), followed by carbon (17.7 percent), and iron (9.7 percent). Various metals make up the tiny remainder of that two percent. This uneven and scale-free type of distribution is called a power law distribution. It is one of the most universal characteristics of nonlinear networks.
Within a nonlinear network such as the internet, those sites with the most connections have the lowest degree of participation, and the sites that exhibit the highest degree of participation have the fewest links or connections. Take for example Google, Amazon, or other large websites: there are only a few of them participating at that level, so they have the most connection with other websites. Because those few large sites have so many connections, they have more power within the network and their effectiveness to reach other websites within the network is that much stronger. These are the hubs of the network, and they are crucial in supporting the stability and robustness of the whole network. But those sites that have the highest degree of participation, such as the millions of small personal websites, have the fewest connections. In nonlinear networks, the members with higher connectivity in the network have more power and more control over the whole network.
Power Law Distribution of participation and connections among websites
The power law distribution principle applies to all nonlinear networks, including networks within the body that regulate our blood circulation and nervous system, and the networks throughout the rest of our natural world.
For more on how an uneven power law distribution affects nonlinear networks, see Part 2 of the full manuscript: Nonlinear Networks