Higher-order temporal network effects through triplet evolution

TL;DR

This paper introduces a method to analyze the evolution of triplets in temporal networks, demonstrating that higher-order interactions significantly influence network dynamics and improve link prediction accuracy.

Contribution

The paper develops a transition matrix approach to quantify triplet evolution and shows higher-order interactions are essential for understanding real-world network dynamics.

Findings

Higher-order interactions differ from pairwise models in real data.

Triplet dynamics improve link prediction performance.

Different real-world systems exhibit distinct higher-order patterns.

Abstract

We study the evolution of networks through `triplets' - three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm's performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.