Network Diffusion -- Framework to Simulate Spreading Processes in Complex Networks

TL;DR

This paper addresses the need for standardized, reproducible simulations of spreading processes on complex networks by extending the Network Diffusion framework to support temporal and multilayer structures. It surveys existing tools, introduces a comprehensive, framework-oriented library compatible with NetworkX, and demonstrates four case studies (SIR-UA, temporal LTM with CogSNet, multilayer ICM with MDS seeds, and NEM on temporal networks) to illustrate capabilities. Key contributions include a unified environment for defining propagation models, networks, and simulation parameters, plus seed-selection techniques tailored to multilayer systems and a critical appraisal of scalability and limitations. The work advances open science and reproducibility in computational network science by providing implementational details, benchmark experiments, and a path toward standardizing research environments for spreading phenomena.

Abstract

With the advancement of computational network science, its research scope has significantly expanded beyond static graphs to encompass more complex structures. The introduction of streaming, temporal, multilayer, and hypernetwork approaches has brought new possibilities and imposed additional requirements. For instance, by utilising these advancements, one can model structures such as social networks in a much more refined manner, which is particularly relevant in simulations of the spreading processes. Unfortunately, the pace of advancement is often too rapid for existing computational packages to keep up with the functionality updates. This results in a significant proliferation of tools used by researchers and, consequently, a lack of a universally accepted technological stack that would standardise experimental methods (as seen, e.g. in machine learning). This article addresses that issue by presenting an extended version of the Network Diffusion library. First, a survey of the existing approaches and toolkits for simulating spreading phenomena is shown and then, an overview of the framework functionalities. Finally, we report four case studies conducted with the package to demonstrate its usefulness: the impact of sanitary measures on the spread of COVID-19, the comparison of information diffusion on two temporal network models, and the effectiveness of seed selection methods in the task of influence maximisation in multilayer networks. We conclude the paper with a critical assessment of the library and the outline of still awaiting challenges to standardise research environments in computational network science.

Figures (8)

• Figure 1: Graph of states and transitions between them for the spreading model of two processes: contagion (SIR) and awareness of its existence (UA). Each state is represented by two letters indicating the state of both processes, e.g., IU indicates that the node is Infected (I) with the disease and Unaware (U) of its existence. The symbols on the arrows indicates the transition probability from one state to another (for values please see Tab. \ref{['tab:sir_ua']}).
• Figure 2: Infection and Awareness curves for spreading of SIR-UA model within aucs-2 network in three different epidemic regimes where we can observe how different prevention measures lockdown (infection risk reduction by 90% -- $\lambda = 0.1$), wearing masks or 1m social distancing (risk reduction by 65% -- $\lambda = 0.35$), and no measures (no risk reduction -- $\lambda = 1$) affect the number of infected and aware individuals (agents) in the network.
• Figure 3: Infection and Awareness curves for spreading of SIR-UA model within sf-2 network in three different epidemic regimes where we can observe how different prevention measures lockdown ($\lambda = 0.1$), wearing masks or 1m social distancing ($\lambda = 0.35$), and no measures ($\lambda = 1$) affect the number of infected and aware individuals (agents) in the network.
• Figure 4: Infection and Awareness curves for spreading of SIR-UA model within er-2 network in three different epidemic regimes where we can observe how different prevention measures lockdown ($\lambda = 0.1$), wearing masks or 1m social distancing ($\lambda = 0.35$), and no measures ($\lambda = 1$) affect the number of infected and aware individuals (agents) in the network.
• Figure 5: The comparison of a final spread as a percentage of activated nodes for the LTM of social influence for two settings: the temporal network based on the CogSNet model and the aggregated static network for the e-mail exchange data in a manufacturing company. The evaluated parameters were the seeding budget ($\gamma$) and the LTM threshold ($\mu$).