Analysis of (ω1, ω2)-Temporal Random Hyperbolic Graphs

Core Concepts

Analyzing the impact of (ω1, ω2) on temporal network properties.

Abstract

The content discusses the extension of a model to allow different connection and disconnection probabilities, providing insights into temporal network dynamics. It covers the distributions of contact and intercontact durations, the expected time-aggregated degree, and the impact on epidemic spreading processes. The analysis involves the Appell F1 series and Gauss hypergeometric functions.
I. Introduction

Model introduction for human contact networks.
Key properties of the dynamic-S1 model.
II. Preliminaries

Overview of the S1 model.
Network generation steps.
III. (ω1, ω2)-Dynamic-S1

Model description and connection probabilities.
Equilibrium connection probability analysis.
IV. Distribution of Contact Durations

Derivation of contact duration distribution.
Analysis of the average contact duration.
V. Distribution of Intercontact Durations

Derivation of intercontact duration distribution.
Analysis of the average intercontact duration.
VI. Time-Aggregated Degree

Calculation of the expected time-aggregated degree.
Impact of ω1, ω2, and T on the time-aggregated degree.

Stats

"The average snapshot degree converges to its target value ¯ k = 5 before slot 100."
"Results are presented for different levels of the link persistence probability ω1, while in all cases ω2 = 0."
"Results are shown for different values of the network temperature T."

Quotes

"Spreading performance is affected by the network temperature T, with lower values of T suppressing spreading."
"The average contact duration increases as either ω1 or ω2 increases."

Key Insights Distilled From

$(ω_1, ω_2)$-Temporal random hyperbolic graphs

by Sofoclis Zam... at arxiv.org 03-27-2024

https://arxiv.org/pdf/2403.17440.pdf

Deeper Inquiries

How do different values of T impact the spreading performance in temporal networks

Different values of T impact the spreading performance in temporal networks by influencing the localization of connections. A lower T value favors connections at smaller effective distances, leading to increased clustering in the network. This localization can slow down spreading by reducing the opportunities for nodes to connect and infect others. On the other hand, higher T values increase randomness in connections, which can lead to a more widespread spreading of epidemics. Therefore, the choice of T plays a crucial role in determining the speed and extent of spreading processes in temporal networks.

What are the implications of the model's assumptions on link persistence probabilities for real-world applications

The model's assumptions on link persistence probabilities have significant implications for real-world applications, especially in the context of epidemic spreading and network dynamics. By allowing connections and disconnections to persist with different probabilities (ω1 and ω2), the model provides a more nuanced representation of temporal network dynamics. This flexibility enables researchers to explore the impact of varying levels of link persistence on spreading phenomena. In real-world applications, such as epidemiological studies or social network analysis, understanding how connections persist or dissolve over time can provide valuable insights into the dynamics of information dissemination, disease spread, and network resilience.

How can the findings of this study be applied to other dynamic network models or systems

The findings of this study can be applied to other dynamic network models or systems to enhance our understanding of temporal network dynamics and their impact on spreading processes. By incorporating distinct persistence probabilities for connections and disconnections, researchers can better model the evolving nature of real-world networks. This approach can be extended to study various phenomena, such as information diffusion, opinion formation, or resource allocation, in dynamic networks. The insights gained from this study can also inform the design of more realistic network models that capture the complexities of temporal interactions and their implications for system behavior.