ESTIMATION OF POWER-LAW EXPONENT OF DEGREEDISTRIBUTION USING MEAN VERTEX DEGREE

摘要

The power-law exponent -y describing the form of the degree distribution of networks isrelated to the mean degree of the networks. This relation provides a useful method toestimate this exponent because mean degrees can easily be obtained by the number ofvertices and edges in the networks. We improved the relation obtained only by ordinaryintegral approximation, and examined its availability for number of vertices, minimumdegree considered, and range of y, taking also into consideration the number of verticeswith minimum degree. As a result, we were able to estimate slight deviations of y from3, which are usually observed in numerical simulations of growing networks with linearpreferential attachment. Furthermore, using this method, we were also able to predictto what extent y changed by joining pre-existing vertices in growing networks or byimposing restrictions to prevent the gaining of new edges for certain vertices. For caseswhere -γ <2, weestimated the power-law exponent of degree distributions networksformed by traces of random walkers from the increased rate of vertices with creatededges.