  We investigate the mean-field dynamics of stochastic McKean differential
equations with heterogeneous particle interactions described by large network
structures. To express a wide range of graphs, from dense and sparse
structures, we incorporate the recently developed graph limit theory of
graphops into the limiting McKean-Vlasov equations. Global stability of the
splay steady state is proven via a generalized entropy method, leading to
explicit graph-structure dependent decay rates. We further analyze the
limitations of the methodology and provided examples of random graphs such as
power law graphs.
