含表决系统的网络联络矩阵的一种降阶方法

为了解决含有表决子系统的网络系统在转化为网络图时增加大量重复弧和重复节点，使网络的联络矩阵变为一个高阶稀疏矩阵的问题，提出了一种降阶方法．此法针对该稀疏矩阵的特点进行分块，使表决子系统对应于分块矩阵中的一个矩阵块；引入矩阵的对角乘法算子和对角还原算子，对表决子系统对应的矩阵块进行独立运算．运算结果表明，该方法使联络矩阵明显降阶．

Reduced-Order Method for Connection Matrix in Network with Voting Systems

To solve the problem that the order of a connection matrix is greatly increased because a large number of repeated nodes and links are resulted in when a network with voting systems is changed into a network graph, a reduced-order method was proposed. In this method, the connection matrix are divided into block matrixes on the basis of its characteristics, so a voting sub-system is corresponding to a block matrix, and the block matrix corresponding to the voting system is operated independently by defining and using two matrix operators. The calculated result shows that this method can reduce the order of a connection matrix greatly.