Furuya S, Yakubo K
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):066104. doi: 10.1103/PhysRevE.78.066104. Epub 2008 Dec 5.
An analysis to describe statistical properties of weighted complex networks is proposed. Effective structures of weighted networks depend on how strongly weights w are paid attention or which weights are relevant to the network problem. Defining the metaweight w;{q} with a real parameter q , we characterize systematically weighted complex networks depending on the level of importance of weights. It is found that power-law distribution functions R_{q}[s(q)] of metastrengths s(q) defined by s_{i}(q)= summation operator_{j}w_{ij};{q} , where i and j denote node indices for any q are characterized by only three exponents if the weight distribution is independent of network topology. We also examine the validity of our analytical arguments and the meaning of power-law forms of R_{q}[s(q)] for different q values by illustrating some examples.
提出了一种用于描述加权复杂网络统计特性的分析方法。加权网络的有效结构取决于权重(w)被关注的强度，或者哪些权重与网络问题相关。通过用实参数(q)定义元权重(w_{i}^{(q)})，我们根据权重的重要性水平系统地表征加权复杂网络。研究发现，如果权重分布与网络拓扑无关，由(s_{i}(q)=\sum_{j}w_{ij}^{(q)})定义的元强度(s(q))的幂律分布函数(R_{q}[s(q)])（其中(i)和(j)表示任意(q)的节点索引）仅由三个指数表征。我们还通过举例说明了我们分析论证的有效性以及不同(q)值下(R_{q}[s(q)])幂律形式的含义。
