May-31-2017

Chapter 6-1: 80/20 Rule

80% of the land was owned by only 20% of the population in Italy.

80% of the profits are produced by 20% of the employees.

80% of the customer service problems are created by only 20% of the customers.

80% of the crime is committed by 20% of criminals. 

In most cases, 80% of our efforts are largely irrelevant. 

Chapter 6-2: The power-law distribution

A power-law distribution is a continuously decreasing curve, implying that too many small events coexist with a few large events. 

Page 70: Scale 标度

As shown in the Bell Curve below (left), in a random network, the peak of the distribution implies that the vast majority of nodes have the same number of links and that nodes deviating from the average are extremely rare.

A random network has the characteristic of "scale" in its node connectivity, embodied by the average node and fixed by the peak of the degree distribution.

A power-law degree distribution is scale-free. There is no intrinisic scale in networks with power-law degree distribution. Most network in nature have a power-law degree distribution. 

The slowly decaying power-law distribution predicts that each scale-free network will have several large hubs that will fundementally define the network's topology. The scale-free give legitimacy to hubs, which determines the structural stability, dynamic behavior, robustness, and error and attack tolerance of real networks. They stand as proof of highly important orginizaing principles that govern network evolution. 

Chapter 6-3: Phase transition

Phase transition: e.g., water from liquid to gas, magma freeze into rock, a metal become a magnet, follow the mysterious power laws. Near the critical point, just when the phase transition take place, i,e., order emerges from disorder, all quantities of interest follow power laws characterized by critical exponents.