Double power-law degree distribution and informational entropy in urban road networks

摘要

The double power-law function, p(x) ～ 1/(x~b + cx ~d) where x is the degree of one node, and b, c, d are parameters, is used to fit the degree distribution of urban road network of Le Mans city in France. It is called "double power-law" since it behaves as two power laws respectively, in large and small degree region with a crossing in-between. The position of the crossing point is derived as a function of the three parameters. The probabilistic uncertainty of this law is studied with two possible information measures: a generalized measure called varentropy and the Shannon entropy formula.