We propose and analyze a novel nonparametric goodness-of-fit testing procedure for ex-changeable exponential random graph model (ERGM) when a single network realization is observed. The test determines how likely it is that the observation is generated from a target unnormalized ERGM density. Our test statistics are derived of kernel Stein discrepancy, a divergence constructed via Stein’s method using functions from a reproducing kernel Hilbert space (RKHS), combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test using simulated networks from the target ERGM. We show theoretical properties for the testing procedure w.r.t a class of ERGM. Simulation studies and real network applications are presented