# Stream Graphs and Link Streams for the Modeling of Interactions over Time

arXiv: https://arxiv.org/abs/1710.04073 · HTML: https://mlsanity.com/paper/1710.04073/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 14 of 14)

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- [Longitudinal Modularity, a Modularity for Link Streams](https://mlsanity.com/paper/2408.16877/) (2024)
- [Robust Dynamic Network Embedding via Ensembles](https://mlsanity.com/paper/2105.14557/) (2021)
- [Sparse-Dyn: Sparse Dynamic Graph Multi-representation Learning via Event-based Sparse Temporal Attention Network](https://mlsanity.com/paper/2201.01384/) (2022)
- [SimHawNet: A Modified Hawkes Process for Temporal Network Simulation](https://mlsanity.com/paper/2203.07260/) (2022)
- [Exploring the Performance of Continuous-Time Dynamic Link Prediction Algorithms](https://mlsanity.com/paper/2405.17182/) (2024)
- [Exploring and mining attributed sequences of interactions](https://mlsanity.com/paper/2107.13329/) (2021)
- [A Frequency-Structure Approach for Link Stream Analysis](https://mlsanity.com/paper/2212.03804/) (2022)
- [Characterizing Information Shared by Participants to Coding Challenges: The Case of Advent of Code](https://mlsanity.com/paper/2412.02290/) (2024)
- [Discovering Communities in Continuous-Time Temporal Networks by Optimizing L-Modularity](https://mlsanity.com/paper/2510.00741/) (2025)
- [Trivial Graph Features and Classical Learning are Enough to Detect Random Anomalies](https://mlsanity.com/paper/2603.01841/) (2026)
- [Conditional Entropy of Heat Diffusion on Temporal Networks](https://mlsanity.com/paper/2605.21514/) (2026)
- [Early Language Learning via Spreading Activation and Category Exploration in Complex Networks](https://mlsanity.com/paper/2607.06258/) (2026)

## Abstract (arXiv)

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher-level objects such as quotient graphs, line graphs, k-cores, and centralities. This paper also considers discrete versus continuous time assumptions, instantaneous links, and extensions to more complex cases.