超网络能量研究与应用

图能量是图论研究的重要内容,图能量及其变种已在无向图、有向图、混合图等其他多种类型的图中得到很多成功的应用.超网络是一类较传统意义上的复杂网络更为复杂的网络.大多数图能量均是基于矩阵特征值计算得到的,无法推广应用到超网络中,应用范围受限.基于网络维数的网络能量已先后应用于无向图、有向图等多种类型图的分析研究中,并与无向...

Research and Application of Hypernetwork Energy

Graph energy plays an important role in research of graph theory.Graph energy and many other similar variants have been applied in many other types of graphs,e.g.,undirected graphs,oriented graphs,mixed graphs,and so on.Hypernetwork is a kind of network which is more complex than traditional complex network.Most graph energies are calculated based on the eigenvalues of matrix and can hardly be extended to hypernetwork,which limits their application range.Network energy based on network dimension has been applied in undirected graphs and oriented graphs one by one,and is closely related to many other energy-like quantities,e.g.,graph energy of undirected graphs,skew energy of oriented graphs,and so on.In this paper,based on hypernetwork dimension of hypernetwork and combined with network energy,hypernetwork energy of hypernetwork is proposed with application of hypernetwork dimension on hypernetwork.At the same time,several upper and lower limits of hypernetwork energy are given,and the internal relations between hypernetwork energy of hypernetwork and network energy of graphs are demonstrated.Finally,several important properties of hypernetwork energy are analyzed as well.