论文标题
具有Q指数分布的随机网络
Random networks with q-exponential degree distribution
论文作者
论文摘要
我们使用配置模型来生成具有遵循$ q $ - 指数的度分布的网络，$ p_q（k）=（2-q）λ[1-（1- q）λk]^{1/（q-1）} $，对于参数$ q $和$λ$的任意值。我们研究了这些网络的分类性和最短路径，发现分布越类似于纯幂定律，相应的节点的连接越差。实际上，最近一个邻居的平均程度以$λ^{ - 1} $单调生长。此外，我们的结果表明，$ Q $ - 指数网络比随机失败和恶意攻击更强大，而不是标准的无标度网络。实际上，删除节点的关键要素以$λ^{ - 1} $的攻击而对数增长，以实现恶意攻击。对$ k_s $ core分解的分析表明，$ q $ - 指数网络具有最高的$ k_s $ core，它更大，并且比纯无标度网络具有更大的$ k_s $。同时，具有$ Q $ - 指数分布的网络表现出无标度和小世界的属性，使其成为在多种系统中应用的模型。
We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)λ[1-(1-q)λk]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $λ$. We study the assortativity and the shortest path of these networks finding that the more the distribution resembles a pure power law, the less well connected are the corresponding nodes. In fact, the average degree of a nearest neighbor grows monotonically with $λ^{-1}$. Moreover, our results show that $q$-exponential networks are more robust against random failures and against malicious attacks than standard scale-free networks. Indeed, the critical fraction of removed nodes grows logarithmically with $λ^{-1}$ for malicious attacks. An analysis of the $k_s$-core decomposition shows that $q$-exponential networks have a highest $k_s$-core, that is bigger and has a larger $k_s$ than pure scale-free networks. Being at the same time well connected and robust, networks with $q$-exponential degree distribution exhibit scale-free and small-world properties, making them a particularly suitable model for application in several systems.
