论文标题
网络重新布线在$ r $ -K $飞机中
Network rewiring in the $r$-$K$ plane
论文作者
论文摘要
我们通过一种新的重新布线算法在配置模型中生成了相关的无标度网络，该算法允许调整Newman的分类系数$ R $和最近的邻居$ K $的平均度（范围为$ -1 \ le R \ le r \ le r \ le r \ le 1 $，$ k \ ge \ ge \ langle k \ langle k \ rangle rangle $）。在每个尝试的重新布线步骤中，计算本地变化$ΔR$和$ΔK$，然后根据标准大都市概率$ \ exp（\pmΔr/t）$接受该步骤，其中$ t $是可变温度。我们证明了$ΔR$和$ΔK$之间的一般关系，因此在两个变量之间找到了具有截然不同的定义和拓扑含义的连接。我们描述了$ r $ - $ k $平面中的重新布线轨迹，并探索最大的分类和拆卸网络的限制，包括以前尚未考虑的最低最低度（$ k_ {min} \ ge 1 $）的情况。在重新布线中监视巨型组件的大小和网络的熵。分支近似值$ \ bar {z} _ {2，b} $的平均邻居数在重新布线中是恒定的，并且独立于马克维亚网络的相关性。但是，作为该学位的函数，第二邻居的数量提供了有关网络连接性的有用信息，并且也受到监视。
We generate correlated scale-free networks in the configuration model through a new rewiring algorithm which allows to tune the Newman assortativity coefficient $r$ and the average degree of the nearest neighbors $K$ (in the range $-1\le r \le 1$, $K\ge \langle k \rangle$). At each attempted rewiring step, local variations $Δr$ and $ΔK$ are computed and then the step is accepted according to a standard Metropolis probability $ \exp(\pmΔr/T)$, where $T$ is a variable temperature. We prove a general relation between $Δr$ and $ΔK$, thus finding a connection between two variables which have very different definitions and topological meaning. We describe rewiring trajectories in the $r$-$K$ plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ($k_{min} \ge 1$) which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbours in the branching approximation $\bar{z}_{2,B}$ is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.
