DOUBLE POWER-LAW DEGREE DISTRIBUTION AND INFORMATIONAL ENTROPY IN URBAN ROAD NETWORKS

The double power-law function ,p(x) similar to 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.