Iterative structural coarse-graining for contagion dynamics in complex networks (2412.20503v1)

Abstract: Contagion dynamics in complex networks drive critical phenomena such as epidemic spread and information diffusion,but their analysis remains computationally prohibitive in large-scale, high-complexity systems. Here, we introduce the Iterative Structural Coarse-Graining (ISCG) framework, a scalable methodology that reduces network complexity while preserving key contagion dynamics with high fidelity. Importantly, we derive theoretical conditions ensuring the precise preservation of both macroscopic outbreak sizes and microscopic node-level infection probabilities during network reduction. Under these conditions, extensive experiments on diverse empirical networks demonstrate that ISCG achieves significant complexity reduction without sacrificing prediction accuracy. Beyond simplification, ISCG reveals multiscale structural patterns that govern contagion processes, enabling practical solutions to longstanding challenges in contagion dynamics. Specifically, ISCG outperforms traditional adaptive centrality-based approaches in identifying influential spreaders, immunizing critical edges, and optimizing sentinel placement for early outbreak detection, offering superior accuracy and computational efficiency. By bridging computational efficiency with dynamical fidelity, ISCG provides a transformative framework for analyzing large-scale contagion processes, with broad applications for epidemiology, information dissemination, and network resilience.

• The paper introduces the ISCG framework that reduces network complexity while preserving macroscopic outbreak sizes and microscopic infection probabilities.
• It employs an iterative merging of k-cliques into super-nodes, ensuring both global structure and local contagion dynamics are maintained.
• Quantitative tests show ISCG outperforms traditional methods in influence maximization, edge-based immunization, and sentinel surveillance applications.

Overview of "Iterative Structural Coarse-Graining for Contagion Dynamics in Complex Networks"

The paper "Iterative Structural Coarse-Graining for Contagion Dynamics in Complex Networks" introduces the Iterative Structural Coarse-Graining (ISCG) framework, a methodological advancement aimed at simplifying complex networks while maintaining the fidelity of contagion dynamics. This framework is significant in the field of network science, particularly where high complexity in network structures poses computational challenges for real-time analysis and decision-making in scenarios like epidemic response and information diffusion.

ISCG presents a scalable approach that leverages local structural information to reduce network complexity, focusing on $k$-cliques within the network. The framework simplifies networks by iteratively merging maximal cliques into super-nodes, each retaining essential contagion characteristics. This method ensures that both macroscopic (global structure) and microscopic (node-level dynamics) features are preserved across a reduced network. Importantly, ISCG offers theoretical conditions under which it maintains the macroscopic outbreak sizes and microscopic infection probabilities. The conditions specify a minimum transmission probability $\hat{\beta}_k$, ensuring full contagion within a $k$-clique, and utilize effective transmission probabilities between super-nodes.

Quantitative validations show that ISCG accurately reproduces both macroscopic outbreak sizes and critical contagion transition behaviors, maintaining a high fidelity across various scales of network reduction. The paper demonstrates the framework's applicability using several real-world networks such as those representing scientific collaborations, illustrating substantial reductions in nodes and edges without significant loss of dynamic fidelity. The capacity for both exact and approximate reductions is especially noteworthy, the latter offering a tunable trade-off between further network simplification and contagion fidelity.

ISCG's practical implications are demonstrated through applications in three classical contagion modeling challenges: influence maximization, edge-based immunization, and sentinel surveillance. In these applications, ISCG outperforms traditional centrality-based methods by effectively leveraging coarse-grained network representations to identify critical structural elements like influential nodes and edges. This ability highlights ISCG’s utility in designing effective intervention strategies in real-world networks.

Theoretically, ISCG advances our understanding of the interplay between network structure and dynamics, providing insights into higher-order interactions such as those in simplicial complexes and hypergraphs. By preserving critical contagion dynamics at multiple scales, ISCG offers a robust tool for studying multi-scale network phenomena, including synchronization in coupled oscillators and cascading failures in infrastructure networks.

The framework is not without its challenges. The necessity for full contagion within super-nodes to maintain accuracy might limit the applicability of ISCG in scenarios involving extremely low transmission probabilities. Future research directions could explore the adaptation of ISCG to accommodate non-full contagion dynamics within super-nodes, thereby extending its applicability to a broader range of real-world systems. Additionally, the potential extension of ISCG to non-contagion dynamics presents an exciting avenue for future exploration.

In conclusion, the ISCG framework represents a significant advancement in the analysis of complex networks, providing a scalable, efficient, and accurate method for examining contagion dynamics. Its theoretical rigor, coupled with practical flexibility, positions it as a valuable framework for addressing a wide range of challenges in network science, from theoretical investigations to practical applications in epidemic modeling and beyond.