# Mining Persistent Activity in Continually Evolving Networks

arXiv: https://arxiv.org/abs/2006.15410 · HTML: https://mlsanity.com/paper/2006.15410/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2020.

## Built on by (most cited first, 13 of 13)

- [Anomaly Detection in Dynamic Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2406.00134/) (2024)
- [Sketch-Based Anomaly Detection in Streaming Graphs](https://mlsanity.com/paper/2106.04486/) (2021)
- [PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts](https://mlsanity.com/paper/2101.07152/) (2021)
- [odeN: Simultaneous Approximation of Multiple Motif Counts in Large Temporal Networks](https://mlsanity.com/paper/2108.08734/) (2021)
- [Anomaly Detection in Graph Structured Data: A Survey](https://mlsanity.com/paper/2405.06172/) (2024)
- [GraphAnoGAN: Detecting Anomalous Snapshots from Attributed Graphs](https://mlsanity.com/paper/2106.15504/) (2021)
- [Isconna: Streaming Anomaly Detection with Frequency and Patterns](https://mlsanity.com/paper/2104.01632/) (2021)
- [Leveraging the Graph Structure of Neural Network Training Dynamics](https://mlsanity.com/paper/2111.05410/) (2021)
- [Online Detection of Anomalies in Temporal Knowledge Graphs with Interpretability](https://mlsanity.com/paper/2408.00872/) (2024)
- [ARES: Anomaly Recognition Model For Edge Streams](https://mlsanity.com/paper/2511.22078/) (2025)
- [A Hidden Challenge of Link Prediction: Which Pairs to Check?](https://mlsanity.com/paper/2102.07878/) (2021)
- [Efficient Approximate Temporal Triangle Counting in Streaming with Predictions](https://mlsanity.com/paper/2506.13173/) (2025)
- [Adaptive-GraphSketch: Real-Time Edge Anomaly Detection via Multi-Layer Tensor Sketching and Temporal Decay](https://mlsanity.com/paper/2509.11633/) (2025)

## Abstract (arXiv)

Frequent pattern mining is a key area of study that gives insights into the structure and dynamics of evolving networks, such as social or road networks. However, not only does a network evolve, but often the way that it evolves, itself evolves. Thus, knowing, in addition to patterns' frequencies, for how long and how regularly they have occurred---i.e., their persistence---can add to our understanding of evolving networks. In this work, we propose the problem of mining activity that persists through time in continually evolving networks---i.e., activity that repeatedly and consistently occurs. We extend the notion of temporal motifs to capture activity among specific nodes, in what we call activity snippets, which are small sequences of edge-updates that reoccur. We propose axioms and properties that a measure of persistence should satisfy, and develop such a persistence measure. We also propose PENminer, an efficient framework for mining activity snippets' Persistence in Evolving Networks, and design both offline and streaming algorithms. We apply PENminer to numerous real, large-scale evolving networks and edge streams, and find activity that is surprisingly regular over a long period of time, but too infrequent to be discovered by aggregate count alone, and bursts of activity exposed by their lack of persistence. Our findings with PENminer include neighborhoods in NYC where taxi traffic persisted through Hurricane Sandy, the opening of new bike-stations, characteristics of social network users, and more. Moreover, we use PENminer towards identifying anomalies in multiple networks, outperforming baselines at identifying subtle anomalies by 9.8-48% in AUC.