Weighted Path homology of Weighted Digraphs and Persistence
Algebraic Topology
2019-10-23 v1
Abstract
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 homology. We prove a persistent version of a Kunneth-type formula for joins of weighted digraphs.
Keywords
Cite
@article{arxiv.1910.09891,
title = {Weighted Path homology of Weighted Digraphs and Persistence},
author = {Yong Lin and Shiquan Ren and Chong Wang and Jie Wu},
journal= {arXiv preprint arXiv:1910.09891},
year = {2019}
}