Francesco Tudisco

Associate Professor (Reader) in Machine Learning

School of Mathematics, The University of Edinburgh
The Maxwell Institute for Mathematical Sciences
School of Mathematics, Gran Sasso Science Institute JCMB, King’s Buildings, Edinburgh EH93FD UK
email: f dot tudisco at

Quantifying the structural stability of simplicial homology

Nicola Guglielmi, Anton Savostianov, Francesco Tudisco,
Journal of Scientific Computing, 97 : (2023)


The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current work, we study the stability in terms of the smallest perturbation sufficient to change the dimensionality of the corresponding homology group. Such definition requires an appropriate weighting and normalizing procedure for the boundary operators acting on the Hodge algebra’s homology groups. Using the resulting boundary operators, we then formulate the question of structural stability as a spectral matrix nearness problem for the corresponding higher-order graph Laplacian. We develop a bilevel optimization procedure suitable for the formulated matrix nearness problem and illustrate the method’s performance on a variety of synthetic quasi-triangulation datasets and transportation networks.

Please cite this paper as:

  title={Quantifying the structural stability of simplicial homology},
  author={Guglielmi, N. and Savostianov, A. and Tudisco, F.},

Links: arxiv doi code

Keywords: simplicial complex higher-order networks networks spectral clustering eigenvalue optimization graph Laplacian Hodge Laplacian