# Topological analysis of the connectome of digital reconstructions of neural microcircuits

arXiv: https://arxiv.org/abs/1601.01580 · HTML: https://mlsanity.com/paper/1601.01580/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2016.

## Built on by (most cited first, 15 of 15)

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- [Novel definition and quantitative analysis of branch structure with topological data analysis](https://mlsanity.com/paper/2402.07436/) (2024)
- [Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learning](https://mlsanity.com/paper/2412.05132/) (2024)
- [Opportunities and challenges in partitioning the graph measure space of real-world networks](https://mlsanity.com/paper/2106.10753/) (2021)
- [Beyond holography: the entropic quantum gravity foundations of image processing](https://mlsanity.com/paper/2503.14048/) (2025)
- [Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding](https://mlsanity.com/paper/2505.17939/) (2025)
- [Persistent reachability homology in machine learning applications](https://mlsanity.com/paper/2511.04825/) (2025)
- [Persistence-Augmented Neural Networks](https://mlsanity.com/paper/2604.08469/) (2026)
- [T-SNN: Temporal Simplicial Neural Network for EEG Decoding](https://mlsanity.com/paper/2609.34002/) (2026)

## Abstract (arXiv)

A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons (H. Markram, et al., Reconstruction and simulation of neocortical microcircuitry, Cell, 163 (2015) no. 2, 456-492). Since traditional graph-theoretical methods may not be sufficient to understand the immense complexity of such a biological network, we explored whether methods from algebraic topology could provide a new perspective on its structural and functional organization. Structural topological analysis revealed that directed graphs representing connectivity among neurons in the microcircuit deviated significantly from different varieties of randomized graph. In particular, the directed graphs contained in the order of 107 simplices DH groups of neurons with all-to-all directed connectivity. Some of these simplices contained up to 8 neurons, making them the most extreme neuronal clustering motif ever reported. Functional topological analysis of simulated neuronal activity in the microcircuit revealed novel spatio-temporal metrics that provide an effective classification of functional responses to qualitatively different stimuli. This study represents the first algebraic topological analysis of structural connectomics and connectomics-based spatio-temporal activity in a biologically realistic neural microcircuit. The methods used in the study show promise for more general applications in network science.