基于邻接矩阵准平方法网络拓扑分析

摘要

The principle of network topology by matrix method is to determine the connectivity of two nodes rather than the level of the connectivity. It will be fast if the element of the connectivity matrix and its symmetrical element are updated as soon as the element is calculated for involving the new connectivity of the nodes in the multiplication. According to the above thought, a network topology by quasi-square of the adjacency matrix is presented. Only one time of matrix multiplication is required by the presented method to achieve a connectivity matrix which is not a full connectivity matrix but can reveal network topology sufficiently, and then the network is gained by reverse row sweep. So the speed of network topology is increased. The correctness of the proposed method is proved theoretically, and its effectiveness is validated by a practical network.%矩阵法网络拓扑的本质是确定网络中各节点是否连通,并不需要明确是几级连通.因此每计算出连通矩阵的一个元素可以及时更新该元素及其对称元素,使节点间的最新连通关系参与计算,有利于提高计算速度.基于此思想,提出了基于邻接矩阵准平方法的网络拓扑分析方法.该方法仅需对邻接矩阵进行一次矩阵平方运算,所得到的连通矩阵虽不是全连通矩阵,但足以反映网络拓扑关系,然后使用逆序行扫描法就可得到网络分析结果,提高了矩阵法网络拓扑分析的速度.该方法的正确性在理论上得到了证明,它的有效性也为实际大型电网的拓扑分析所验证.