Revisiting the Edges Dissolution Approximation

We study the edges dissolution approximation (EDA) of Carnegie et al. We begin by repeating an observation from Carnegie et al., namely that in the dyad-independent case, the exact result is tractable. We then observe that taking the sparse limit of the exact result leads to a different approximation than that in Carnegie et al. We prove that this new approximation is better than the old approximation for sparse dyad-independent models, and we show via simulation that the new approximation tends to perform better than the old approximation for sparse models with sufficiently weak dyad-dependence. We then turn to general dyad-dependent models, proving that both the old and new approximations are asymptotically exact as the time step size goes to zero, for arbitrary dyad-dependent terms and some dyad-dependent constraints. In demonstrating this result, we identify a Markov chain, defined for any sufficiently small time step, whose cross-sectional and durational behavior is exactly that we desire of the EDA. This Markov chain can be simulated, and we do so for a dyad-dependent model, showing that it eliminates the biases present with either of the dyad-independent-derived approximations.