论文标题
多路复用网络上的较弱的渗透，边缘重叠
Weak percolation on multiplex networks with overlapping edges
论文作者
论文摘要
我们解决具有重叠边缘的多重网络的弱渗透问题。在弱渗透中，如果至少在该组件中的每个层中的至少一个邻居中的一个邻居中，则属于连接的组件。与相互依存的网络中的相互连接的组件相比，这是一个弱条件，在该网络中，必须通过每个层中的路径连接任何两个顶点。重叠对弱渗透的影响与巨型相互连接的分量相反。尽管对于巨大的相互联系的组件，重叠并没有改变关键现象，但我们的理论表明，在两层重叠的两层浓度中，重叠的任何（非零）浓度将弱渗透过渡到普通的渗透普遍性类别。在三层中，问题的相图包含两条线 - 连续过渡和不连续的线 - 根据各层重叠的方式，以各种方式连接。如果仅翻一番边缘，这些线的两个终点是重合的，从而产生了异质$ k $ core渗透中类似的三个智力点。
We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a weaker condition than for a mutually connected component in interdependent networks, in which any two vertices must be connected by a path within each of the layers. The effect of the overlaps on weak percolation turns out to be opposite to that on the giant mutually connected component. While for the giant mutually connected component, overlaps do not change the critical phenomena, our theory shows that in two layers any (nonzero) concentration of overlaps drives the weak percolation transition to the ordinary percolation universality class. In three layers, the phase diagram of the problem contains two lines -- of a continuous phase transition and of a discontinuous one -- connected in various ways depending on how the layers overlap. In the case of only doubled overlapped edges, two of the end points of these lines coincide, resulting in a tricritical point like that seen in heterogeneous $k$-core percolation.
