Weighted chained graphs and some applications

This paper introduces weighted chained graphs, as well as minimal broadcasting and receiving sets, and investigates their properties. Both directed and undirected graphs are considered. The notion of central nodes is introduced both for weighted directed and undirected graphs. This notion is helpful for determining how quickly information can propagate throughout a graph. In particular, it is useful for the investigation of transportation networks and for city planning. Applications to the analysis of airline and bus networks are presented.