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Creators/Authors contains: "Reichel, Lothar"

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  1. Abstract

    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$$\{\ell ,k\}$${,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.

     
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    Abstract This paper introduces the notions of chained and semi-chained graphs. The chain of a graph, when existent, refines the notion of bipartivity and conveys important structural information. Also the notion of a center vertex $$v_c$$ v c is introduced. It is a vertex, whose sum of p powers of distances to all other vertices in the graph is minimal, where the distance between a pair of vertices $$\{v_c,v\}$$ { v c , v } is measured by the minimal number of edges that have to be traversed to go from $$v_c$$ v c to v . This concept extends the definition of closeness centrality. Applications in which the center node is important include information transmission and city planning. Algorithms for the identification of approximate central nodes are provided and computed examples are presented. 
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