Multifractal properties of growing networks
Multifractal properties of growing networks
复制标题
生长网络的多重分形特性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Mendes
中科院分区：
文献类型：
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作者：
S. Dorogovtsev;A. N. Samukhin;J. Mendes
我们引入了一系列用于不断发展的网络的新模型。在这些网络中，新边优先附加到具有更多连接数的顶点，并且新顶点由已存在的顶点创建，部分继承（部分复制）其父级的连接。我们证明这两个特征的组合产生了多重分形度分布。这里的度是一个顶点的连接数。对于此类的非平凡模型，找到了精确的多重分形分布。在无限网络极限下，分布趋于幂律形式 Π(q) ~ q−γ，其中 γ = (2)1/2。对于有限网络，由于多重分形，任何将分布解释为无标度的尝试都将导致指数 γ 的值不明确。
We introduce a new family of models for growing networks. In these networks new edges are preferentially attached to vertices with a higher number of connections, and new vertices are created by already existing ones, partially inheriting (partially copying) connections of their parents. We show that the combination of these two features produces multifractal degree distributions. Here degree is the number of connections of a vertex. An exact multifractal distribution is found for a nontrivial model of this class. The distribution tends to a power law form Π(q) ~ q−γ with γ = (2)1/2 in the infinite network limit. For finite networks, because of multifractality, any attempt to interpret the distribution as scale free will result in an ambiguous value of the exponent γ.