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In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the $\phi$-weighted coboundary operator induced by a weight function $\phi$.
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Yanhua Li and Zhi-Li Zhang, Random walks on digraphs, the generalized digraph laplacian and the degree of asymmetry , International Workshop on Algorithms and Models for the Web-Graph, Springer, 2010, pp. 74–85
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2012
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Ali Masoudi-Nejad, Falk Schreiber, and Zahra Razaghi Moghadam Kashani, Building blocks of biological networks: a review on major network motif discovery algorithms , IET Systems Biology 6
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2017
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Owen T. Courtney and Ginestra Bianconi, Weighted growing simplicial complexes , Physical Review E 95
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2017
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Ankit Sharma, Terrence J. Moore, Ananthram Swami, and Jaideep Srivastava, Weighted simplicial complex: A novel approach for predicting small group evolution , Pacific-Asia Conference on Knowledge Discovery and Data Mining, Springer, 2017, pp. 511–523
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Zixuan Cang, Lin Mu, and Guo-Wei Wei, Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening , PLoS computational biology 14
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