Nonextensive maximum-entropy approach to small-world networks

The degree distribution P (k) in complex networks has been obtained by maximizing the nonextensive information entropy with the three constraints: < 1 >= 1, < k >= μ and < k >= ρ, where <> denotes the average over P (k). The distribution P (k) is expressed by a generalized Gaussian (referred to as Q-Gaussian) which has a maximum at k = μ with a width proportional to √ ρ− μ2, in contrast to a conventional q-Gaussian with a maximum at the zero value. It has been shown that Q-Gaussian well describes the degree distribution in small-world networks. An alternative, differential-equation approach to Q-Gaussian is discussed also. PACS No.05.90.+m, 89.75.-k,89.70.+c