Chained structure of directed graphs with applications to social and transportation networks

The need to determine the structure of a graph arises in many applications. This paper studies directed graphs and defines the notions of $\ell$ -chained and $\{\ell ,k\}$ -chained directed graphs. These notions reveal structural properties of directed graphs that shed light on how the nodes of the graph are connected. Applications include city planning, information transmission, and disease propagation. We also discuss the notion of in-center and out-center vertices of a directed graph, which are vertices at the center of the graph. Computed examples provide illustrations, among which is the investigation of a bus network for a city.