中介驱动型依恋网络的动态标度、数据崩溃和自相似性
Dynamic Scaling, Data-collapse and Self-Similarity in Mediation-Driven Attachment Networks
摘要：
最近，我们证明了如果Barabási-Albert（BA）网络的$i$第th节点由广义度$q_i(t)=k_i(t)t_i^β/m$刻画，其中$k_i(t)\sim t^β$和$m$是它在当前时刻$t$和出生时刻$t_i$的度，那么相应的分布函数$F(q,t)$表现出动态标度.将同样的想法应用于我们最近提出的中介驱动的连接（MDA）网络，我们发现它也表现出动态缩放，但与BA模型不同，MDA模型的指数$β$假设了一个值谱$1/2\leq β\leq 1$。此外，我们发现，小$m$的标度曲线是显着不同的较大的$m$和BA网络也是如此，虽然在较小的程度上。我们使用的想法，分布的逆调和平均值（IHM）的邻居，每个节点，并表明，遵循幂律度分布的数据点的数量增加的偏度的IHM分布减少。最后，我们表明，MDA和BA模型变得几乎相同的大$m$。
英文摘要：
Recently, we have shown that if the $i$th node of the Barabási-Albert (BA) network is characterized by the generalized degree $q_i(t)=k_i(t)t_i^β/m$, where $k_i(t)\sim t^β$ and $m$ are its degree at current time $t$ and at birth time $t_i$, then the corresponding distribution function $F(q,t)$ exhibits dynamic scaling. Applying the same idea to our recently proposed mediation-driven attachment (MDA) network, we find that it too exhibits dynamic scaling but, unlike the BA model, the exponent $β$ of the MDA model assumes a spectrum of value $1/2\leq β\leq 1$. Moreover, we find that the scaling curves for small $m$ are significantly different from those of the larger $m$ and the same is true for the BA networks albeit in a lesser extent. We use the idea of the distribution of inverse harmonic mean (IHM) of the neighbours of each node and show that the number of data points that follow the power-law degree distribution increases as the skewness of the IHM distribution decreases. Finally, we show that both MDA and BA models become almost identical for large $m$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
