Pseudofractal scale-free web
Pseudofractal scale-free web
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DOI：
10.1103/physreve.65.066122
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发表时间：
2002-06-01
影响因子：
2.4
通讯作者：
Mendes, JFF
中科院分区：
文献类型：
--
作者：
Dorogovtsev, SN;Goltsev, AV;Mendes, JFF
我们发现，无标度随机网络是很好的建模简单的确定性图。我们的图具有离散度分布（度是顶点的连接数），其特征在于幂律，指数为gamma=1+ln 3/ln 2。这种紧凑结构的性质令人惊讶地接近那些增长的随机无标度网络，其伽马值在最有趣的区域，在2和3之间。我们成功地找到准确和数值高精度的所有主要特征的图形。特别地，我们得到了精确的最短路径长度分布。对于一个大的网络（ln N>>1），分布趋向于一个宽度类似于以（-）lsimilar to ln N为中心的高斯分布。我们证明了图的邻接矩阵的特征值谱具有指数为2+gamma的幂律尾。
We find that scale-free random networks are excellently modeled by simple deterministic graphs. Our graph has a discrete degree distribution (degree is the number of connections of a vertex), which is characterized by a power law with exponent gamma=1+ln 3/ln 2. Properties of this compact structure are surprisingly close to those of growing random scale-free networks with gamma in the most interesting region, between 2 and 3. We succeed to find exactly and numerically with high precision all main characteristics of the graph. In particular, we obtain the exact shortest-path-length distribution. For a large network (ln N>>1) the distribution tends to a Gaussian of width similar torootln N centered at (-)lsimilar toln N. We show that the eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail with exponent 2+gamma.