# Memory in network flows and its effects on spreading dynamics and community detection

arXiv: https://arxiv.org/abs/1305.4807 · HTML: https://mlsanity.com/paper/1305.4807/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2013.

## Built on by (most cited first, 18 of 18)

- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs](https://mlsanity.com/paper/2209.08311/) (2022)
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- [Deep Ensembles for Graphs with Higher-order Dependencies](https://mlsanity.com/paper/2205.13988/) (2022)
- [Community Recovery in the Geometric Block Model](https://mlsanity.com/paper/2206.11303/) (2022)
- [The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks](https://mlsanity.com/paper/2310.01144/) (2023)
- [Weisfeiler and Leman Follow the Arrow of Time: Expressive Power of Message Passing in Temporal Event Graphs](https://mlsanity.com/paper/2505.24438/) (2025)
- [Predicting Influential Higher-Order Patterns in Temporal Network Data](https://mlsanity.com/paper/2107.12100/) (2021)
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- [Differentially Private Synthetic Graphs Preserving Triangle-Motif Cuts](https://mlsanity.com/paper/2507.14835/) (2025)
- [Understanding Parallel Samplers in Masked Diffusion via Random Walks on Graphs](https://mlsanity.com/paper/2606.22976/) (2026)
- [Thematic recommendations on knowledge graphs using multilayer networks](https://mlsanity.com/paper/2105.05733/) (2021)
- [Uncovering the Origins of Instability in Dynamical Systems: How Attention Mechanism Can Help?](https://mlsanity.com/paper/2212.09641/) (2022)
- [Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs](https://mlsanity.com/paper/2301.11120/) (2023)
- [FlowHON: Representing Flow Fields Using Higher-Order Networks](https://mlsanity.com/paper/2312.02243/) (2023)
- [Representing Outcome-driven Higher-order Dependencies in Graphs of Disease Trajectories](https://mlsanity.com/paper/2312.15353/) (2023)
- [A temporal graph dissimilarity measure capturing epidemic spreading behavior](https://mlsanity.com/paper/2610.16456/) (2026)

## Abstract (arXiv)

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it ignores a potentially important feature of the dynamics: where flow moves to may depend on where it comes from. Here we analyse pathways from different systems, and while we only observe marginal consequences for disease spreading, we show that ignoring the effects of second-order Markov dynamics has important consequences for community detection, ranking, and information spreading. For example, capturing dynamics with a second-order Markov model allows us to reveal actual travel patterns in air traffic and to uncover multidisciplinary journals in scientific communication. These findings were achieved only by using more available data and making no additional assumptions, and therefore suggest that accounting for higher-order memory in network flows can help us better understand how real systems are organized and function.