有向网络上的加权渗流
Weighted percolation on directed networks
摘要：
我们提出了一个分析的渗流过渡的一般节点删除策略有效的局部树状有向网络。启发式参数的基础上，我们预测，如果删除节点$i$的概率是$p_i$，网络解体，如果$p_i$是这样的矩阵与条目$A_{ij}(1-p_i)$的最大特征值小于1，其中$A$是网络的邻接矩阵。马尔可夫网络模型的知识或适用性是不需要我们的理论，从而使其适用于以前的作品没有涵盖的情况。我们测试我们预测的渗流准则对不同的网络和节点删除策略的数值结果。
英文摘要：
We present an analysis of the percolation transition for general node removal strategies valid for locally tree-like directed networks. On the basis of heuristic arguments we predict that, if the probability of removing node $i$ is $p_i$, the network disintegrates if $p_i$ is such that the largest eigenvalue of the matrix with entries $A_{ij}(1-p_i)$ is less than 1, where $A$ is the adjacency matrix of the network. The knowledge or applicability of a Markov network model is not required by our theory, thus making it applicable to situations not covered by previous works. We test our predicted percolation criterion against numerical results for different networks and node removal strategies.
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。
