# Predicting Influential Higher-Order Patterns in Temporal Network Data

arXiv: https://arxiv.org/abs/2107.12100 · HTML: https://mlsanity.com/paper/2107.12100/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 14 of 14)

- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [The why, how, and when of representations for complex systems](https://mlsanity.com/paper/2006.02870/) (2020)
- [Memory in network flows and its effects on spreading dynamics and community detection](https://mlsanity.com/paper/1305.4807/) (2013)
- [Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers](https://mlsanity.com/paper/1409.7017/) (2014)
- [Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks](https://mlsanity.com/paper/1307.4030/) (2013)
- [Representing higher-order dependencies in networks](https://mlsanity.com/paper/1508.03113/) (2015)
- [When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks](https://mlsanity.com/paper/1702.05499/) (2017)
- [Mapping higher-order network flows in memory and multilayer networks with Infomap](https://mlsanity.com/paper/1706.04792/) (2017)
- [Modeling sequences and temporal networks with dynamic community structures](https://mlsanity.com/paper/1509.04740/) (2015)
- [Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities](https://mlsanity.com/paper/1508.06467/) (2015)
- [HONEM: Learning Embedding for Higher Order Networks](https://mlsanity.com/paper/1908.05387/) (2019)
- [HoNVis: Visualizing and Exploring Higher-Order Networks](https://mlsanity.com/paper/1702.00737/) (2017)
- [Effect of Memory on the Dynamics of Random Walks on Networks](https://mlsanity.com/paper/1401.0447/) (2014)
- [Predicting Sequences of Traversed Nodes in Graphs using Network Models with Multiple Higher Orders](https://mlsanity.com/paper/2007.06662/) (2020)

## Built on by (most cited first, 1 of 1)

- [Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs](https://mlsanity.com/paper/2301.11120/) (2023)

## Abstract (arXiv)

Networks are frequently used to model complex systems comprised of interacting elements. While edges capture the topology of direct interactions, the true complexity of many systems originates from higher-order patterns in paths by which nodes can indirectly influence each other. Path data, representing ordered sequences of consecutive direct interactions, can be used to model these patterns. On the one hand, to avoid overfitting, such models should only consider those higher-order patterns for which the data provide sufficient statistical evidence. On the other hand, we hypothesise that network models, which capture only direct interactions, underfit higher-order patterns present in data. Consequently, both approaches are likely to misidentify influential nodes in complex networks. We contribute to this issue by proposing five centrality measures based on MOGen, a multi-order generative model that accounts for all indirect influences up to a maximum distance but disregards influences at higher distances. We compare MOGen-based centralities to equivalent measures for network models and path data in a prediction experiment where we aim to identify influential nodes in out-of-sample data. Our results show strong evidence supporting our hypothesis. MOGen consistently outperforms both the network model and path-based prediction. We further show that the performance difference between MOGen and the path-based approach disappears if we have sufficient observations, confirming that the error is due to overfitting.