Social Computing with Artificial Intelligence by Xun Liang

Author:Xun Liang
Language: eng
Format: epub, pdf
ISBN: 9789811577604
Publisher: Springer Singapore

So, there must be (assume ),

In other words, the power law distribution function is the only probability distribution function that satisfies the scale-free condition. The derivation of properties is omitted in this book.

In a large scale-free network with proper power law distribution (usually ), the degree of most nodes is relatively low, but there are a few nodes with relatively high degree. Therefore, this kind of network is also called inhomogeneous network, and those relatively high degree nodes are called “hub” of the network. For example, the U.S. highway network can be approximated as a uniform network, because it is impossible to tell hundreds of roads to pass through the same city; while the U.S. air network can be seen as a scale-free network, most airports are small airports, but there are a small number of very large airports connecting many small airports, such as Chicago, Dallas, Atlanta, and New York Airport.

Another way to represent degree data is to draw cumulative degree distribution function,

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