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Motifs in Temporal Networks

arXiv 1612.09259 ↗First posted 29 Dec 2016cs.SI physics.soc-ph stat.MLcited by 101

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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.

Key facts. Cited by 101 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Dec 2016.

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Citing papers per year: 2021: 24; 2022: 15; 2023: 16; 2024: 17; 2025: 20; 2026: 9.

101 papers.

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  1. 2021Inductive Representation Learning in Temporal Networks via Causal Anonymous Walkscited by 188
  2. 2021Dynamic Network Embedding Surveycited by 44
  3. 2024TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphscited by 35
  4. 2023Temporal and Heterogeneous Graph Neural Network for Financial Time Series Predictioncited by 30
  5. 2024A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challengescited by 29
  6. 2023TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discoverycited by 27
  7. 2021Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernelscited by 19
  8. 2021Motif Prediction with Graph Neural Networkscited by 18
  9. 2022TIGGER: Scalable Generative Modelling for Temporal Interaction Graphscited by 18
  10. 2022Towards Sparsification of Graph Neural Networkscited by 18
  11. 2021Edge Proposal Sets for Link Predictioncited by 16
  12. 2021Graph Neural Networks: Methods, Applications, and Opportunitiescited by 16
38 more
  1. 2023Classification of Edge-dependent Labels of Nodes in Hypergraphscited by 14
  2. 2024SLADE: Detecting Dynamic Anomalies in Edge Streams without Labels via Self-Supervised Learningcited by 14
  3. 2021Neural Predicting Higher-order Patterns in Temporal Networkscited by 13
  4. 2022Graph Sequential Neural ODE Process for Link Prediction on Dynamic and Sparse Graphscited by 13
  5. 2024Higher-order Structure Based Anomaly Detection on Attributed Networkscited by 12
  6. 2024Binary Search with Distributional Predictionscited by 11
  7. 2021Adversarial Attack Framework on Graph Embedding Models with Limited Knowledgecited by 10
  8. 2022Piecewise-Velocity Model for Learning Continuous-time Dynamic Node Representationscited by 10
  9. 2023DYMOND: DYnamic MOtif-NoDes Network Generative Modelcited by 10
  10. 2023Topology-Agnostic Detection of Temporal Money Laundering Flows in Billion-Scale Transactionscited by 10
  11. 2022Time-aware Dynamic Graph Embedding for Asynchronous Structural Evolutioncited by 8
  12. 2022BeGin: Extensive Benchmark Scenarios and An Easy-to-use Framework for Graph Continual Learningcited by 8
  13. 2023Using Motif Transitions for Temporal Graph Generationcited by 7
  14. 2024Enhancing Cross-domain Link Prediction via Evolution Process Modelingcited by 7
  15. 2021A Multi-purposed Unsupervised Framework for Comparing Embeddings of Undirected and Directed Graphscited by 6
  16. 2025A Survey of Link Prediction in Temporal Networkscited by 6
  17. 2021ConTIG: Continuous Representation Learning on Temporal Interaction Graphscited by 5
  18. 2021Task and Model Agnostic Adversarial Attack on Graph Neural Networkscited by 5
  19. 2023Online List Labeling with Predictionscited by 5
  20. 2021Updating Embeddings for Dynamic Knowledge Graphscited by 4
  21. 2021Modelling Direct Messaging Networks with Multiple Recipients for Cyber Deceptioncited by 4
  22. 2021Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrastcited by 4
  23. 2021Dynamic Representation Learning with Temporal Point Processes for Higher-Order Interaction Forecastingcited by 4
  24. 2022The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networkscited by 4
  25. 2022A Survey on Temporal Graph Representation Learning and Generative Modelingcited by 4
  26. 2022DyG2Vec: Efficient Representation Learning for Dynamic Graphscited by 4
  27. 2023Using Time-Aware Graph Neural Networks to Predict Temporal Centralities in Dynamic Graphscited by 4
  28. 2024Retrofitting Temporal Graph Neural Networks with Transformercited by 4
  29. 2025LLMTM: Benchmarking and Optimizing LLMs for Temporal Motif Analysis in Dynamic Graphscited by 4
  30. 2021PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Countscited by 3
  31. 2021Learning low-rank latent mesoscale structures in networkscited by 3
  32. 2021IACN: Influence-aware and Attention-based Co-evolutionary Network for Recommendationcited by 3
  33. 2021odeN: Simultaneous Approximation of Multiple Motif Counts in Large Temporal Networkscited by 3
  34. 2022ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networkscited by 3
  35. 2022Scalable Motif Counting for Large-scale Temporal Graphscited by 3
  36. 2023Temporal Motifs for Financial Networks: A Study on Mercari, JPMC, and Venmo Platformscited by 3
  37. 2023MPool: Motif-Based Graph Poolingcited by 3
  38. 2023arXiv4TGC: Large-Scale Datasets for Temporal Graph Clusteringcited by 3

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