发表机构
The Open University of Israel; Bar-Ilan University; Yeshiva University（以色列开放大学; 巴伊兰大学; 叶史瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究一维长程多重网络中相互巨组分的涌现，给出临界值下界和树近似，发现网络稳定性低于单层，且相变阶次随σ变化。
AI 中文摘要
我们研究了一个由晶格上的两个一维长程网络组成的多重网络中相互巨组分的涌现。一个晶格上两个节点之间的距离为$r$，它们之间以边相连的概率随距离代数衰减为$Cr^{-(1+\sigma)}$，其中$0 < \sigma < 1$且$0 < C \leq 1$。若$C > C_c^{\mathrm{mul}}$，则存在相互巨组分，其中$C_c^{\mathrm{mul}}(\sigma)$是依赖于$\sigma$的$C$的临界值。我们找到了$C_c^{\mathrm{mul}}$的严格下界，以及一种树近似，其对$C_c^{\mathrm{mul}}$的估计在$\sigma \leq 0.5$时与模拟结果在0.6%以内吻合。多重网络明显比单网络情况更不稳定，这从$C_c^{\mathrm{mul}}$的较大值可以看出，其值高达单层值的2.4倍。我们的模拟表明，转变的阶次依赖于$\sigma$。对于$\sigma \leq 0.35$，相互巨组分在一级相变中突然崩溃，而对于$\sigma \geq 0.4$，转变是连续的。当依赖链接连接随机节点对时，对于所有$\sigma$，转变都是一级的。
英文摘要
We study the emergence of a mutual giant component in a multiplex network comprised of two one-dimensional long-range networks on a lattice. The probability that two nodes on one lattice, with a distance $r$ between them, are connected with an edge falls algebraically with distance as $Cr^{-(1+σ)}$, where $0 < σ< 1$ and $0 < C \leq 1$. A mutual giant component exists if $C > C_c^{\mathrm{mul}}$, where $C_c^{\mathrm{mul}}(σ)$ is a critical value of $C$ that is dependent on $σ$. We find rigorous lower bounds on $C_c^{\mathrm{mul}}$, and a tree approximation whose estimate of $C_c^{\mathrm{mul}}$ agrees with simulations within 0.6% for $σ\leq 0.5$. The multiplex network is significantly less stable than the single network case, as is evident by the larger value of $C_c^{\mathrm{mul}}$, which is up to 2.4 times the single-layer value. Our simulations indicate that the order of the transition depends on $σ$. For $σ\leq 0.35$ the mutual giant component collapses abruptly, in a first-order phase transition, while for $σ\geq 0.4$ the transition is continuous. When the dependency links connect random pairs of nodes, the transition is first order for all $σ$.
Comments12 pages, 4 figures, 1 table
