Correlated Growth of Causal Networks

The study of causal structure in complex systems has gained increasing attention, with many recent studies exploring causal networks that capture cause-effect relationships across diverse fields. Despite increasing empirical evidence linking causal structures to network topological correlations, the mechanisms underlying the emergence of these correlations in causal networks remain poorly understood. In this work, we propose a general growth framework for causal networks, incorporating two key types of correlations: causal and dynamic. We analytically demonstrate that degree correlations emerge as a consequence of marginal dependencies on these correlations. Our theoretical predictions align quantitatively with empirical data from four large-scale innovation networks. Our theory not only sheds light on the origins of topological correlations but also provides a general framework for understanding correlated growth across causal systems.