• Corpus ID: 204823741

Weighted Path homology of Weighted Digraphs and Persistence

  title={Weighted Path homology of Weighted Digraphs and Persistence},
  author={Yong Lin and Shiquan Ren and Chong Wang and Jie Wu},
  journal={arXiv: Algebraic Topology},
In recent years, A. Grigor'yan, Y. Lin, Y. Muranov and S.T. Yau [6, 7, 8, 9] constructed a path homology theory for digraphs. Later, S. Chowdhury and F. Memoli [3] studied the persistent path homology for directed networks. In this paper, we generalize the path homology theory for digraphs and construct a weighted path homology for weighted digraphs. We study the persistent weighted path homology for weighted digraphs and detect the effects of the weights on the persistent weighted path… 

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