14. Scale-free Networks

We’re doing a series on the book “Linked: How Everything is Connected to Everything Else and What It Means for Business, Science, and Everyday Life” by Albert-Laszlo Barabasi.

WARNING: If you want to comment on any of these articles, please read the previous articles to understand the foundation.

The previous article explained how Hubs operate according to a Power Law.

Power Law: a few large events/members account for most of the action/activity

Bell curves: signature of Random Networks

Power laws: signature of real world Networks

Let’s look at the differences between Random/Regular Networks and Power Law Networks. Mr. Barabasi writes:

“The striking visual and structural differences between a random network and one described by a power-law degree distribution are best seen by comparing a U.S. road map with an airline routing map.”

A roadmap looks closer to a grid. The map of airline flights absolutely follows a Power Law where a handful of airports handle the majority of flights. However, there is more to the structure than this upper level.

“The largest hub is closely followed by two or three somewhat smaller hubs, followed by dozens that are even smaller, and so on, eventually arriving at the numerous small nodes. The power law distribution thus forces us to abandon the idea of a scale, or a characteristic node.”

A Random or Regular network can be represented on one level. We say this is “Single Scale”. (See left half of graphic)

Power Laws create scales at various levels: Large Hubs, Medium Hubs, Small Hubs. We say this is “Scale-free”.

Scale-free: a Network that isn’t limited to being represented at a single level

In the graphic, the Network to the right resembles a corporation. The red Node is the CEO who directly interacts with the C-Suite. The green C-Suite Nodes interact directly with their executives.

In the Synthesis #9 article, we saw how we can represent each Scale with a circle. The three concentric circles (red inside green inside blue) is the Synthesis representation of this Scale-free Network.

Another term is “fractal”.

Fractal: a geometric figure, each part of which has the same statistical character as the whole

Simply put, a fractal is a pattern that is the same regardless of what level (Scale) it's viewed at. Scale-free!

There is one more implication of Networks that operate according to a Power Law.

“Power laws rarely emerge in systems completely dominated by a roll of the dice. Physicists have learned that most often they signal a transition from disorder to order.”

Power laws “are the patent signatures of self-organization in complex systems.”

“We had finally learned that when giving birth to order, complex systems divest themselves of their unique features and display a universal behavior that has similar characteristics in a wide range of systems.” Synthesis!

Next Article: 15. Dr. Barabasi’s Discovery

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