Estimating Formation Mechanisms and Degree Distributions in Mixed Attachment Networks

Abstract

We propose a probabilistic framework to estimate how random and preferential attachment jointly drive growth in evolving directed networks. The method formalizes a time-varying likelihood and establishes conditions under which local maxima exist despite changing connection probabilities during network expansion. Under these conditions, an expectation-maximization approach yields convergent parameter estimates and recovers the contribution of each attachment mechanism. We also derive analytical in-degree distributions and show, through simulation, agreement between theory and observed stationary behavior. The result is a practical inference framework for understanding and modeling network formation in real-world complex systems.