$(\omega_1, \omega_2)$-temporal random hyperbolic graphs

Sofoclis Zambirinis; Fragkiskos Papadopoulos

doi:10.1103/physreve.110.024309

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arXiv · 2403.17440

$(\omega_1, \omega_2)$-temporal random hyperbolic graphs

Sofoclis Zambirinis·Fragkiskos Papadopoulos

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Abstract

We extend a recent model of temporal random hyperbolic graphs by allowing connections and disconnections to persist across network snapshots with different probabilities, $\omega_1$ and $\omega_2$. This extension, while conceptually simple, poses analytical challenges involving the Appell $F_1$ series. Despite these challenges, we are able to analyze key properties of the model, which include the distributions of contact and intercontact durations, as well as the expected time-aggregated degree. The incorporation of $\omega_1$ and $\omega_2$ enables more flexible tuning of the average contact and intercontact durations, and of the average time-aggregated degree, providing a finer control for exploring the effect of temporal network dynamics on dynamical processes. Overall, our results provide new insights into the analysis of temporal networks and contribute to a more general representation of real-world scenarios.

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physics.soc-ph cond-mat.stat-mech cs.SI

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Sofoclis Zambirinis, Fragkiskos Papadopoulos. 2024-03-26. $(\omega_1, \omega_2)$-temporal random hyperbolic graphs. https://doi.org/10.1103/physreve.110.024309

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