Temporal connection probabilities in real networks

TL;DR

This paper introduces a non-Markovian model for predicting link formation in complex networks, integrating geometry and memory effects, validated on real data.

Contribution

It derives a closed-form expression for connection probabilities that combines latent geometry with long-range memory, advancing temporal network forecasting.

Findings

Quantitative agreement with empirical connection probabilities

Geometry and memory jointly influence link dynamics

Provides a minimal, extensible framework for probabilistic forecasting

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.