# Motifs in Temporal Networks

arXiv: https://arxiv.org/abs/1612.09259 · HTML: https://mlsanity.com/paper/1612.09259/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2016.

## Built on by (most cited first, 30 of 101)

- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Dynamic Network Embedding Survey](https://mlsanity.com/paper/2103.15447/) (2021)
- [TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphs](https://mlsanity.com/paper/2406.09639/) (2024)
- [Temporal and Heterogeneous Graph Neural Network for Financial Time Series Prediction](https://mlsanity.com/paper/2305.08740/) (2023)
- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discovery](https://mlsanity.com/paper/2310.19324/) (2023)
- [Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels](https://mlsanity.com/paper/2104.02995/) (2021)
- [Motif Prediction with Graph Neural Networks](https://mlsanity.com/paper/2106.00761/) (2021)
- [TIGGER: Scalable Generative Modelling for Temporal Interaction Graphs](https://mlsanity.com/paper/2203.03564/) (2022)
- [Towards Sparsification of Graph Neural Networks](https://mlsanity.com/paper/2209.04766/) (2022)
- [Edge Proposal Sets for Link Prediction](https://mlsanity.com/paper/2106.15810/) (2021)
- [Graph Neural Networks: Methods, Applications, and Opportunities](https://mlsanity.com/paper/2108.10733/) (2021)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [SLADE: Detecting Dynamic Anomalies in Edge Streams without Labels via Self-Supervised Learning](https://mlsanity.com/paper/2402.11933/) (2024)
- [Neural Predicting Higher-order Patterns in Temporal Networks](https://mlsanity.com/paper/2106.06039/) (2021)
- [Graph Sequential Neural ODE Process for Link Prediction on Dynamic and Sparse Graphs](https://mlsanity.com/paper/2211.08568/) (2022)
- [Higher-order Structure Based Anomaly Detection on Attributed Networks](https://mlsanity.com/paper/2406.04690/) (2024)
- [DYMOND: DYnamic MOtif-NoDes Network Generative Model](https://mlsanity.com/paper/2308.00770/) (2023)
- [Binary Search with Distributional Predictions](https://mlsanity.com/paper/2411.16030/) (2024)
- [Adversarial Attack Framework on Graph Embedding Models with Limited Knowledge](https://mlsanity.com/paper/2105.12419/) (2021)
- [Piecewise-Velocity Model for Learning Continuous-time Dynamic Node Representations](https://mlsanity.com/paper/2212.12345/) (2022)
- [Topology-Agnostic Detection of Temporal Money Laundering Flows in Billion-Scale Transactions](https://mlsanity.com/paper/2309.13662/) (2023)
- [Time-aware Dynamic Graph Embedding for Asynchronous Structural Evolution](https://mlsanity.com/paper/2207.00594/) (2022)
- [BeGin: Extensive Benchmark Scenarios and An Easy-to-use Framework for Graph Continual Learning](https://mlsanity.com/paper/2211.14568/) (2022)
- [Using Motif Transitions for Temporal Graph Generation](https://mlsanity.com/paper/2306.11190/) (2023)
- [Enhancing Cross-domain Link Prediction via Evolution Process Modeling](https://mlsanity.com/paper/2402.02168/) (2024)
- [A Multi-purposed Unsupervised Framework for Comparing Embeddings of Undirected and Directed Graphs](https://mlsanity.com/paper/2112.00075/) (2021)
- [A Survey of Link Prediction in Temporal Networks](https://mlsanity.com/paper/2502.21185/) (2025)
- [ConTIG: Continuous Representation Learning on Temporal Interaction Graphs](https://mlsanity.com/paper/2110.06088/) (2021)
- [Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast](https://mlsanity.com/paper/2112.08733/) (2021)

## Abstract (arXiv)

Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to understanding the structure and function of these systems. However, the role of network motifs in temporal networks, which contain many timestamped links between the nodes, is not yet well understood. Here we develop a notion of a temporal network motif as an elementary unit of temporal networks and provide a general methodology for counting such motifs. We define temporal network motifs as induced subgraphs on sequences of temporal edges, design fast algorithms for counting temporal motifs, and prove their runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to a baseline method. Furthermore, we use our algorithms to count temporal motifs in a variety of networks. Results show that networks from different domains have significantly different motif counts, whereas networks from the same domain tend to have similar motif counts. We also find that different motifs occur at different time scales, which provides further insights into structure and function of temporal networks.