Epidemic spreading on complex networks with community structures (1611.06092v1)

Abstract: Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network, while the other model only preserves the set of communities and the vertex degrees. These models show that community structure is an important determinant of the behavior of percolation processes on networks, such as information diffusion or virus spreading: the community structure can both \textit{enforce} as well as \textit{inhibit} diffusion processes. Our models further show that it is the mesoscopic set of communities that matters. The exact internal structures of communities barely influence the behavior of percolation processes across networks. This insensitivity is likely due to the relative denseness of the communities.

• The paper introduces two novel graph models (HCM and HCM*) that integrate mesoscopic community structures to accurately predict epidemic dynamics.
• It demonstrates that community structures, rather than micro-scale details, predominantly determine the size of the giant component and percolation processes in complex networks.
• The findings provide actionable insights for designing epidemic control strategies and enhancing immunization policies in networked systems.

Epidemic Spreading on Complex Networks with Community Structures

This paper explores the significant influence of community structures on epidemic spreading in complex networks, presenting two random graph models designed to mirror the community properties of real-world networks. These models, the Hierarchical Configuration Model (HCM) and its variant HCM*, focus on the community structure's mesoscopic scale, which comprises subsets of nodes that are densely connected internally and more sparsely connected externally. The findings provide valuable insights into how such structures regulate dynamics like information diffusion and virus propagation.

Overview of the Models

The HCM preserves the exact intra-community connections of the original network while randomizing inter-community edges. In contrast, HCM* randomizes both intra- and inter-community edges while maintaining the proportional distribution of communities and vertex degrees. These models extend the classical configuration model by incorporating community structure, thereby addressing the limitations seen when using only degree distributions to understand epidemic dynamics.

Key Findings

1. Component Size: Analyses show that both models accurately predict the size of the giant component in networks akin to real-world examples, outperforming the classical configuration model. This indicates that the community structure substantially influences network connectivity and robustness.
2. Percolation Processes: Various percolation processes validate the models’ effectiveness in mirroring real-world network behavior. Particularly, bond percolation results suggest that mesoscopic community structures predominantly drive epidemic spread, with the internal community link details being less critical than previously assumed.
3. Sensitivity to Structure: While microscale features like clustering coefficients differ between the models and actual networks, for processes such as epidemic spreading, the mesoscopic structure proves sufficient to capture dynamics effectively. This elucidates a surprising insensitivity to exact intra-community link configurations.
4. Community-Inhibited Percolation: The paper identifies cases where communities act as inhibitors or facilitators of percolation. This nuanced role underscores the complexity underpinning community influence, which can vary significantly across different types of networks.

Implications and Future Directions

The insights from this research present potential applications in designing strategies for controlling epidemic transmission, enhancing immunization policies, and optimizing viral message diffusion. Theoretical implications suggest a shift towards mesoscopic-focused analyses for understanding complex network behaviors beyond traditional scale-free assumptions.

Future developments could explore overlapping community structures and their effects, potentially leading to even more accurate models for networks with intricate overlapping community patterns. Additionally, extending these findings to account for dynamics like targeted attacks further elucidates the role of community structures under varying conditions.

In sum, this paper is a notable contribution to understanding epidemic dynamics in complex networks, advocating for a paradigm shift towards models that incorporate mesoscopic community properties. The analytical tractability and empirical validation of HCM and HCM* represent substantial steps forward in the area of network epidemiology.