Boguñá Marián, Pastor-Satorras Romualdo
Departament de Física Fonamental, Universitat de Barcelona, Avenida Diagonal 647, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):047104. doi: 10.1103/PhysRevE.66.047104. Epub 2002 Oct 21.
We study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node's connectivities. For the case of Markovian complex networks, showing only correlations between pairs of nodes, we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links, which from a node with connectivity k go to nodes with connectivity k('). Numerical simulations on a correlated growing network model provide support for our conclusions.
我们研究了复杂网络上流行病传播的动力学模型，其中节点的连通性之间存在明确的相关性。对于马尔可夫复杂网络的情况，仅显示节点对之间的相关性，我们发现流行病阈值与连通性矩阵的最大特征值成反比，该矩阵给出了平均链接数，即从具有连通性k的节点到具有连通性k(')的节点的链接数。在相关增长网络模型上的数值模拟为我们的结论提供了支持。
