On Spectral Theory of Hypergraphs via Tensors

In the study of complex networks, we encounter an important area of multidisciplinary research, including mathematics, physics, chemistry, biology, social sciences, and information science. All of these networks are actually directed or non-directed graphs. In some cases the data is so complex that not all communications can be considered using a graph, in which case a hypergraph structure is used. A hypergraph is a generalization of a graph in which each edge can contain more than two vertices.Since many properties of hypergraphs such as connectivity, analytic connectivity, vertex cut, chromatic number, etc, can be analyzed based on their spectral properties, the study of spectral theory of hypergraphs has been considered by many researchers in recent years and many works has been done in this area. In this book we study the spectral theory of hypergraphs via their corresponding tensors.