Correlated Growth of Causal Networks

Summary

The study proposes a general growth framework for causal networks, incorporating causal and dynamic correlations. It analytically solves the model for degree correlation and validates theoretical predictions against empirical data from four large-scale innovation networks.

Highlights

• Causal networks capture cause-effect relationships across diverse fields.
• The study proposes a general growth framework for causal networks.
• The framework incorporates causal and dynamic correlations.
• The model is analytically solved for degree correlation.
• Theoretical predictions are validated against empirical data from innovation networks.
• The study sheds light on the origins of topological correlations in causal networks.
• The framework provides a unified approach for modeling correlated growth in causal networks.

Key Insights

• Causal networks are inherently rigid due to the immutability of past events, represented by directed acyclic graphs (DAGs).
• The growth process of causal networks exhibits time-translation invariance (TTI), allowing for the prediction of an exponential growth factor.
• The study introduces a mean-field causal kernel to capture causal correlations, enabling the calculation of the stationary state distribution and network growth rate.
• The framework reduces the parameter space from individual papers to a small set of global parameters, decreasing complexity from O(N) to O(1).
• The theoretical predictions of network growth rates and degree distributions align with empirical measurements from citation graphs.
• The study highlights the importance of considering both causal and dynamical correlations in understanding the evolution of complex networks.
• The proposed framework has the potential to impact various fields, including physics, economics, social sciences, and evolutionary biology.

Mindmap

Citation

Liu, J., Tamang, K., Wang, D., & Song, C. (2024). Correlated Growth of Causal Networks (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.16647