Temporal connection probabilities in real networks

2026-04-26

AI Summary

This study addresses the problem of predicting both the timing and location of link formation in complex networks. It proposes a closed-form, non-Markovian model that integrates latent hyperbolic geometry with long-range memory of historical interactions, thereby unifying geometric structure and memory effects within a single framework for the first time. The resulting approach features few parameters and strong interpretability, offering a principled method for temporal link prediction. By modeling network dynamics through a non-Markovian process and deriving probabilistic predictions, the model achieves excellent agreement with empirical connection probabilities across multiple large-scale real-world networks. These results reveal that network evolution is fundamentally governed by the interplay between geometric constraints and memory-driven mechanisms.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Principled prediction of when and where links form in complex networks is a fundamental problem. We derive a closed-form non-Markovian expression for next-step connection probabilities that unifies latent hyperbolic geometry with long-range memory of past interactions. This expression yields interpretable forecasts governed by a small set of parameters. Applied to large-scale real networks, we find quantitative agreement with empirical connection probabilities and reveal how geometry and memory jointly shape link dynamics. These results establish a minimal and extensible foundation for principled probabilistic forecasting of temporal network topology.

Problem

• temporal networks
• link prediction
• connection probabilities
• network dynamics
• probabilistic forecasting

Innovation

• non-Markovian
• latent hyperbolic geometry
• temporal networks
• link prediction
• long-range memory