Abstract: In the weighted network, the weight of an edge characters the tightness between two nodes, and the degree of a node denotes the number of neighbors of the node. In order to effectively suppress the spread of virus in the weighted networks, an improved Acquaintance Immunization strategy by Considering the Weights and Degrees（AI-CWD） is proposed. In this proposed strategy, the node with highest product between degree and weight will be immunized. And then, simulations are conducted on artificial networks and real networks respectively. Besides, the effect of the proportion of the weight in the product is further studied. The simulation results show that under the circumstance that the densities of immune nodes are the same, the density of infected nodes in the network immunized by the AI-CWD strategy is lower than that of the network immunized by max-weight strategy, the improved acquaintance immunization strategy and the strategy based on ClusterRank algorithm. Namely, the immunization effect of proposed strategy in this paper is better than the other three immunization strategies. A parameter that characters the proportion of weights in the product between degree and weight is also introduced in this paper. Simulation results show that by controlling the parameter in the product, there exits an optimal proportion of weights that can make the density of infected nodes lowest.

Key words: weighted network, acquaintance immunization strategy, BBV network, SI model, virus spread

摘要： 在加权网络中，节点之间的边权值代表节点之间联系的紧密程度，节点的度表示该节点的邻居个数。为了有效抑制加权网络中的病毒传播，提出一种考虑边权和度的熟人免疫策略（AI-CWD）。该策略考虑免疫边权值与度乘积最大的节点，并分别在人工网络和真实网络中对该策略进行了实验分析。同时，进一步研究了边权值和度在乘积中的占比对该策略免疫效果的影响。研究结果表明，在相同的免疫节点密度下，对边权值与度乘积最大的节点进行免疫后网络中感染节点的密度比最大权值免疫、改进的熟人免疫和基于ClusterRank算法免疫的方法要低，亦即AI-CWD免疫效果要优于以上三种免疫策略。并且在相同免疫节点密度下，通过对边权值和度的占比与感染节点密度关系的研究，可以得出：存在一个最优的[α]值，使得最终的感染节点密度最低。

关键词: 加权网络, 熟人免疫, BBV网络, SI模型, 病毒传播