Research and Application of Hypernetwork Energy

Abstract

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.

Keywords

• complex network
• hypernetwork
• graph energy
• network energy
• hypernetwork energy