Community detection on directed networks with missing edges (2410.19651v1)

Abstract: Identifying significant community structures in networks with incomplete data is a challenging task, as the reliability of solutions diminishes with increasing levels of missing information. However, in many empirical contexts, some information about the uncertainty in the network measurements can be estimated. In this work, we extend the recently developed Flow Stability framework, originally designed for detecting communities in time-varying networks, to address the problem of community detection in weighted, directed networks with missing links. Our approach leverages known uncertainty levels in nodes' out-degrees to enhance the robustness of community detection. Through comparisons on synthetic networks and a real-world network of messaging channels on the Telegram platform, we demonstrate that our method delivers more reliable community structures, even when a significant portion of data is missing.

• The paper introduces ΔFS, an extension of the Flow Stability framework that improves community detection in directed networks with incomplete data.
• It integrates uncertainties in node out-degrees and employs a biased teleportation mechanism to adjust the random walk process for missing edges.
• Numerical experiments on synthetic and Telegram network data demonstrate ΔFS's superior performance in accurately recovering true community structures.

Community Detection on Directed Networks with Missing Edges

This paper addresses the challenge of community detection in directed networks with incomplete data. Directed networks, which are commonly used to model systems in technological, biological, and social domains, often suffer from data unreliability due to missing links. This work extends the Flow Stability (FS) framework, originally devised for time-varying networks, to weighted, directed networks with missing edges, proposing a novel methodology named $\Delta$ Flow Stability ($\Delta$FS).

Methodological Advances

The paper capitalizes on known uncertainties in network measurements, specifically uncertainties related to nodes' out-degrees. The extension involves incorporating these uncertainties into the FS framework, which traditionally clusters nodes based on diffusion patterns over time. In $\Delta$FS, an advanced teleportation term is introduced into the forward diffusive process, allowing for a more accurate estimation of the network's community structure despite missing edges.

The transition matrices for the forward and backward diffusion processes are modified to integrate known errors in measured data. In particular, a biased teleportation mechanism adjusts the random walk behavior to account for these inaccuracies, echoing the concept utilized in Bayesian network reconstruction methods.

Numerical Experiments

The paper provides a comparative analysis of $\Delta$FS and traditional FS using synthetic Stochastic Block Model networks and a real-world dataset from Telegram messaging channels. In synthetic networks, $\Delta$FS demonstrates superior performance in recovering the true partitioning of networks, even when a substantial fraction of edges are intentionally removed.

In the Telegram dataset, $\Delta$FS is applied to account for the uncertainty introduced by deleted messages, which can obscure actual network connectivity. The results show that $\Delta$FS identifies the community structure more robustly when compared to FS, especially when a small fraction of edges is missing.

Implications and Future Directions

The implications of this work are significant for empirical studies in areas where data completeness cannot be guaranteed. By enhancing the robustness of community detection algorithms, researchers can derive more reliable insights into the structural and functional organization of complex networks. This becomes especially relevant in social media analysis, biological systems, and any field reliant on network representations of incomplete data.

The proposed method suggests a pathway for further development in several theoretical and practical domains. Future research could expand upon $\Delta$FS by incorporating temporal dynamics and exploring its applicability in multilayer and interconnected network structures.

Conclusion

This paper enriches the FS methodology by addressing data incompleteness, offering valuable insights for improving the robustness of community detection techniques in directed networks. $\Delta$ Flow Stability is a forward step in making network analysis resilient to empirical uncertainties, presenting broader applications across various scientific disciplines.