# Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis

arXiv: https://arxiv.org/abs/2509.08350 · HTML: https://mlsanity.com/paper/2509.08350/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 80 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Network Geometry](https://mlsanity.com/paper/2001.03241/) (2020)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [Clique topology reveals intrinsic geometric structure in neural correlations](https://mlsanity.com/paper/1502.06172/) (2015)
- [Evaluating Overfit and Underfit in Models of Network Community Structure](https://mlsanity.com/paper/1802.10582/) (2018)
- [Persistent Homology of Complex Networks for Dynamic State Detection](https://mlsanity.com/paper/1904.07403/) (2019)
- [The importance of the whole: topological data analysis for the network neuroscientist](https://mlsanity.com/paper/1806.05167/) (2018)
- [Simplicial complexes: higher-order spectral dimension and dynamics](https://mlsanity.com/paper/2001.05934/) (2020)
- [Topological data analysis of contagion maps for examining spreading processes on networks](https://mlsanity.com/paper/1408.1168/) (2014)
- [Detecting the ultra low dimensionality of real networks](https://mlsanity.com/paper/2110.14507/) (2021)
- [A new information dimension of complex networks](https://mlsanity.com/paper/1311.3527/) (2013)
- [Homological Scaffold via Minimal Homology Bases](https://mlsanity.com/paper/2004.11606/) (2020)
- [Random Simplicial Complexes: Models and Phenomena](https://mlsanity.com/paper/2105.12914/) (2021)

## Built on by (most cited first, 1 of 1)

- [Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalization](https://mlsanity.com/paper/2607.27767/) (2026)

## Abstract (arXiv)

Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of communities, impact efficient network navigation, and fundamentally shape connectivity and system behavior. We introduce a topological data analysis weighting scheme for graphs based on chordless cycles to estimate network dimensionality in a data-driven way. We further show that the resulting descriptors can effectively estimate network dimensionality using a neural network architecture trained on a synthetic graph database constructed for this purpose, which requires no retraining to transfer effectively to real-world networks. Thus, by combining cycle-aware filtrations, algebraic topology, and machine learning, our approach provides a robust and effective method for uncovering the hidden geometry of complex networks and guiding accurate modeling and low-dimensional embedding.