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- W2022177848 abstract "The degree of a vertex of a digraph is the number of outgoing edges minus the number of incoming edges. Acyclic digraphs give a model for networks such as citation networks and organizational charts. Motivated by a “local hierarchy theory” developed for this model, we consider the set D ̂ ( δ ) of acyclic digraphs with a specified degree sequence δ . We show that all digraphs in this set can be generated from any one such digraph using just one kind of basic transformation. In the case of degree sequences δ that are minimal in the “Lorenz order”, we investigate the maximum number of edges in an acyclic digraph in D ̂ ( δ ) and show how to construct digraphs in D ̂ ( δ ) with many edges. Determining this maximum number of edges seems to be a very difficult problem." @default.
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- W2022177848 date "2007-03-01" @default.
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- W2022177848 title "Acyclic digraphs and local hierarchy theory" @default.
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- W2022177848 doi "https://doi.org/10.1016/j.mcm.2006.07.012" @default.
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