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Persistent homology of vertex-weighted digraphs. (English) Zbl 1474.55003

Summary: In this paper, we review the homology introduced in a literature, discuss the effects of the weights on the persistent weighted path homology and prove a persistent version of the Künneth formula for joins of vertex-weighted digraphs.

MSC:

55N31 Persistent homology and applications, topological data analysis
05C20 Directed graphs (digraphs), tournaments
05C22 Signed and weighted graphs
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