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line_graph (498B)

      1 # Line graph
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      3 https://en.wikipedia.org/wiki/Line_graph
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      5 The *line graph* of an [undirected_graph] G = (V, E) is the [graph] G' where the [vertices] of G' are E and where there is an edge in G' connecting two edges of E if they share a vertex in G
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      7 They can be recognized in [linear_time]
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      9 They have a [Hamiltonian_cycle] if the original graph has a [Hamiltonian_cycle]: cf [balakrishnan2012textbook], Corollary 6.5.5 and [harary1965eulerian]
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     11 Up: [graph_basic_notions]
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     13 See also: [dual_hypergraph]