Power-law degree distribution of graphs Power-law degree Distributios

"The natural graphs commonly found in the Real-world have, highly skewed Power-law degree distributios ..." is the beginning of the paper, it says. The solution is probably, and then the investigation was known. Power-law degree Distributios is originally a description of the distribution of nodes in the network map, Chinese can be called "Power law degree distribution."

Wikipedia entry "Complex network" in the introduction of "scale-free network", the "Power law degree distribution" can be further understood. The information is explained as follows:

The degree distribution of a network is the probability distribution of the number of nodes connected to this node (the degree of this node) d when randomly extracting a node from the network.
For example: The complete graph distribution of a N-node is: D = n-1 probability is 1, the rest is 0.
The degree distribution of a scale-free network satisfies the power-law distribution, which means that the probability of D = k is proportional to a power of K (generally negative):
\mathbb{p} (d = k) \propto K^{-\alpha}
(= = Add a sentence, this symbol is "proportional to" meaning. Well, I've seen it several times.
The degree distribution of random networks belongs to the normal distribution, so there is a characteristic degree, that is, most of the node's degrees are close to it.
The degree distribution of scale-free networks is distributed: Most of the nodes have fewer connections, and a few nodes have lots of connections. Because there is no degree of feature, hence the name "no scale".
There are many examples of scale-free networks. The Internet, the American actor Network, and the interactive network of proteins in the cell are all scale-free networks. the characteristics of scale-free networks are: When the node is unexpectedly invalid or changed, the impact on the network is generally very small, only a very small probability will have a large impact, but when the distribution node is affected, the network will be more affected than the random network.

To steal a picture of an individual slides. It is clear that 1% of the nodes are connected to half the edges and the remaining half are shared by the remaining 99% nodes.