Dorogovtsev S N, Mendes J F F, Oliveira J G
Departamento de Física da Universidade de Aveiro, Portugal.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 May;73(5 Pt 2):056122. doi: 10.1103/PhysRevE.73.056122. Epub 2006 May 23.
We study the mean length (l)(k) of the shortest paths between a vertex of degree k and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law correction to a logarithmic dependence, (l)(k) = A ln[N/k((gamma-1)/2)]-Ck(gamma-1)/N+ in a wide range of network sizes. Here N is the number of vertices in the network, gamma is the degree distribution exponent, and the coefficients A and C depend on a network. We compare this law with a corresponding (l)(k) dependence obtained for random scale-free networks growing through the preferential attachment mechanism. In stochastic and deterministic growing trees with an exponential degree distribution, we observe a linear dependence on degree, (l)(k)approximately A ln N-Ck. We compare our findings for growing networks with those for uncorrelated graphs.
我们研究了在增长网络中，度为k的顶点与其他顶点之间最短路径的平均长度l(k)，其中相关性至关重要。在许多确定性无标度网络中，我们在广泛的网络规模范围内观察到对对数依赖的幂律修正，即l(k)=A ln[N/k((γ - 1)/2)] - Ck(γ - 1)/N + 。这里N是网络中的顶点数，γ是度分布指数，系数A和C取决于网络。我们将此规律与通过偏好依附机制增长的随机无标度网络所得到的相应l(k)依赖关系进行比较。在具有指数度分布的随机和确定性生长树中，我们观察到度的线性依赖关系，即l(k)≈A ln N - Ck。我们将增长网络的研究结果与不相关图的结果进行比较。
