标题： 具有可调度分布指数的无标度网络 显示英文标题

标题： Scale-free networks with tunable degree distribution exponents

摘要： 我们提出并研究了一个尺度无标度增长网络的模型，该模型给出的度分布由幂律行为主导，且具有依赖于模型的可调节指数。 该模型是基于流行度驱动和适应度驱动优先连接的增长网络的混合体。 当网络增长时，新添加的节点以基于现有节点流行度的概率$p$与现有节点建立$m$条新链接，并以基于现有节点适应度的概率$1-p$建立新链接。 在平均场方法中推导出了度分布$P(p,k)$的显式形式。 对于合理大的$k$和$P(p,k) \sim k^{-\gamma(p)}{\cal F}(k,p)$，函数${\cal F}$由$1/\ln(k/m)$在$p$小值时的行为主导，并在$p \to 1$时变为$k$独立，而$\gamma(p)$是一个模型相关的指数。 度分布和指数$\gamma(p)$被发现与通过广泛数值模拟得到的结果有很好的一致性。 显示英文摘要

摘要： We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes $m$ new links to existing nodes with a probability $p$ based on popularity of the existing nodes and a probability $1-p$ based on fitness of the existing nodes. An explicit form of the degree distribution $P(p,k)$ is derived within a mean field approach. For reasonably large $k$, $P(p,k) \sim k^{-\gamma(p)}{\cal F}(k,p)$, where the function ${\cal F}$ is dominated by the behavior of $1/\ln(k/m)$ for small values of $p$ and becomes $k$-independent as $p \to 1$, and $\gamma(p)$ is a model-dependent exponent. The degree distribution and the exponent $\gamma(p)$ are found to be in good agreement with results obtained by extensive numerical simulations.