Understanding How Network Geometry Influences Diffusion Processes in Complex Networks: A Focus on Cryptocurrency Blockchains and Critical Infrastructure Networks

TL;DR

The paper investigates how network geometry shapes diffusion processes in complex networks, focusing on cryptocurrency blockchains and critical infrastructure networks. It combines KT and SI diffusion models with motif analysis, bootstrap CIs, and Bayesian inference to quantify how topology, motifs, and centrality affect diffusion speed and reach across ER, GRG, DT, SBM, Ethereum, and European power grids. Key findings show hub-dominated networks resist random failures but are vulnerable to targeted attacks, while certain 4-node motifs and high clustering strongly accelerate diffusion; centrality measures consistently modulate transmissibility. The work provides actionable insights for strengthening network resilience, optimizing information flow, and understanding systemic risks in decentralized digital and critical infrastructure systems.

Abstract

This study provides essential insights into how diffusion processes unfold in complex networks, with a focus on cryptocurrency blockchains and infrastructure networks. The structural properties of these networks, such as hub-dominated, heavy-tailed topology, network motifs, and node centrality, significantly influence diffusion speed and reach. Using epidemic diffusion models, specifically the Kertesz threshold model and the Susceptible-Infected (SI) model, we analyze key factors affecting diffusion dynamics. To assess the uncertainty in the fraction of infected nodes over time, we employ bootstrap confidence intervals, while Bayesian credible intervals are constructed to quantify parameter uncertainties in the SI models. Our findings reveal substantial variations across different network types, including Erdős--Rényi networks, Geometric Random Graphs, and Delaunay Triangulation networks, emphasizing the role of network architecture in failure propagation. We identify that network motifs are crucial in diffusion. We highlight that hub-dominated networks, which dominate blockchain ecosystems, provide resilience against random failures but remain vulnerable to targeted attacks, posing significant risks to network stability. Furthermore, centrality measures such as degree, betweenness, and clustering coefficient strongly influence the transmissibility of diffusion in both blockchain and critical infrastructure networks.

Figures (7)

• Figure 1: All 4-node connected network motifs.
• Figure 2: The effect of network structure/topology on the diffusion process. The left panel represents diffusion starting with the top three nodes with the highest degree for $\tau = 0.30$ and the right panel represents the diffusion for $\tau = 0.40$, with their corresponding $95\%$ confidence intervals.
• Figure 3: Ethereum transaction network (left) and its degree distribution with fitted exponential curve (right).
• Figure 4: Spread of node failures in the Ethereum network under diffusion based on the KT model, where gray nodes represent uninfected nodes and red nodes represent infected nodes.
• Figure 5: Comparison of fraction of infected nodes based on the KT model over time steps in Ethereum network under three different initial infection scenarios.