# The why, how, and when of representations for complex systems

arXiv: https://arxiv.org/abs/2006.02870 · HTML: https://mlsanity.com/paper/2006.02870/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2020.

## Built on by (most cited first, 23 of 23)

- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs](https://mlsanity.com/paper/2312.09504/) (2023)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [AHP: Learning to Negative Sample for Hyperedge Prediction](https://mlsanity.com/paper/2204.06353/) (2022)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs](https://mlsanity.com/paper/2209.08311/) (2022)
- [HOT: Higher-Order Dynamic Graph Representation Learning with Efficient Transformers](https://mlsanity.com/paper/2311.18526/) (2023)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Deep Ensembles for Graphs with Higher-order Dependencies](https://mlsanity.com/paper/2205.13988/) (2022)
- [All the World's a (Hyper)Graph: A Data Drama](https://mlsanity.com/paper/2206.08225/) (2022)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learning](https://mlsanity.com/paper/2409.14161/) (2024)
- [Predicting Influential Higher-Order Patterns in Temporal Network Data](https://mlsanity.com/paper/2107.12100/) (2021)
- [One Graph to Rule them All: Using NLP and Graph Neural Networks to analyse Tolkien's Legendarium](https://mlsanity.com/paper/2210.07871/) (2022)
- [Hypergraph clustering using Ricci curvature: an edge transport perspective](https://mlsanity.com/paper/2412.15695/) (2024)
- [Mitigating Data Scarcity in Time Series Analysis: A Foundation Model with Series-Symbol Data Generation](https://mlsanity.com/paper/2502.15466/) (2025)
- [PlasmoData.jl -- A Julia Framework for Modeling and Analyzing Complex Data as Graphs](https://mlsanity.com/paper/2401.11404/) (2024)
- [Characterizing User Archetypes and Discussions on Scored.co](https://mlsanity.com/paper/2407.21753/) (2024)
- [MARIOH: Multiplicity-Aware Hypergraph Reconstruction](https://mlsanity.com/paper/2504.00522/) (2025)
- [Information-theoretic signatures of causality in Bayesian networks and hypergraphs](https://mlsanity.com/paper/2512.20552/) (2025)
- [Conservative Hybrid Graph Networks for Process Systems with Learned Routing](https://mlsanity.com/paper/2608.28896/) (2026)

## Abstract (arXiv)

Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific strategies that are seldom revisited or questioned, and the siloing of ideas within a domain due to inconsistency of complex systems language. In this work we offer basic, domain-agnostic language in order to advance towards a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system and data collected, then moving through different mathematical formalisms for encoding the observed data (i.e. graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each formalism. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of one relation among the parts of a system may influence the existence of another relation. We discuss how dependencies may arise and how they may alter interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and choice of mathematical representation influence the results. We hope this work can serve as an opportunity of reflection for experienced complexity scientists, as well as an introductory resource for new researchers.