网络能量在混合图中的研究与应用

Research and Application of Network Energy on Mixed Graphs

传统的混合图的能量通过对方阵形式的矩阵特征值的计算而得到,难以推广应用到大规模的混合图中.针对这个问题,本文将网络维数应用于混合图中,提出了混合图的网络能量,从而将网络能量从无向图及有向图推广应用到混合图.混合图的网络能量可以通过混合图的节点数目及有向边与无向边的数目而得到,同时给出了混合图的网络能量的若干上下限.在与混合图的Hermitian能量及有向图与无向图的网络能量的对比中分析了所提出的混合图的网络能量的若干重要性质,并论证了无向图、有向图及混合图的网络能量三者之间的内在关联.

The energy of the traditional mixed graph is obtained by calculating the eigenvalues of the matrix in the form of a square matrix,and it is difficult to be extended to large-scale mixed graphs.In response to this problem,this paper applies the network dimension to the mixed graph,and proposes the network energy of the mixed graph,thus the network energy is extended from the undirected graph and the directed graph to the mixed graph.The network energy of a mixed graph can be obtained by the number of nodes and the number of directed and undirected edges of the mixed graph.At the same time,several upper and lower limits of the network energy of the mixed graph are given.Comparied with the Hermitian energy of mixed graph and the network energy of directed and undirected graphs,some important properties of the proposed network energy of the mixed graph are analyzed.The internal relationships among undirected graph,directed graph and mixed graph are also demonstrated.