# Small-World Brain Networks Revisited

arXiv: https://arxiv.org/abs/1608.05665 · HTML: https://mlsanity.com/paper/1608.05665/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2016.

## Built on by (most cited first, 16 of 16)

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- [Dynamic Graph Modeling of Simultaneous EEG and Eye-tracking Data for Reading Task Identification](https://mlsanity.com/paper/2102.11922/) (2021)
- [Building artificial neural circuits for domain-general cognition: a primer on brain-inspired systems-level architecture](https://mlsanity.com/paper/2303.13651/) (2023)
- [Learning Graph Filters for Structure-Function Coupling based Hub Node Identification](https://mlsanity.com/paper/2410.17410/) (2024)
- [BrainHGT: A Hierarchical Graph Transformer for Interpretable Brain Network Analysis](https://mlsanity.com/paper/2511.17604/) (2025)
- [FLYNN: Robust Neural Network for Robot Navigation using Fly Brain Topology](https://mlsanity.com/paper/2607.00025/) (2026)
- [CP-CNN: Core-Periphery Principle Guided Convolutional Neural Network](https://mlsanity.com/paper/2304.10515/) (2023)
- [ElegansNet: a brief scientific report and initial experiments](https://mlsanity.com/paper/2304.13538/) (2023)
- [Generalisation to unseen topologies: Towards control of biological neural network activity](https://mlsanity.com/paper/2407.12789/) (2024)
- [Inference-friendly Graph Compression for Graph Neural Networks](https://mlsanity.com/paper/2504.13034/) (2025)
- [Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators](https://mlsanity.com/paper/2507.21377/) (2025)
- [A Unified Geometric Space for Topological Alignment Between Transformer-Based Models and Human Brain Networks](https://mlsanity.com/paper/2510.24342/) (2025)
- [Structural Graph Probing of Vision-Language Models](https://mlsanity.com/paper/2603.27070/) (2026)

## Abstract (arXiv)

It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.