The paper introduces robust generalized Moran I tests for network-generated cross-sectional dependence in a panel data setting where unit-specific effects can be random or fixed. Network dependence may originate from endogenous variables, exogenous variables, and/or disturbances, and the network dependence is allowed to vary over time. The formulation of the test statistics also aims at accommodating situations where the researcher is unsure about the exact nature of the network. Unit-specific effects are eliminated using the Helmert transformation, which is well known to yield time-orthogonality for linear forms of transformed disturbances. Given the specification of our test statistics, these orthogonality properties also extend to the quadratic forms that underlie our test statistics. This greatly simplifies the expressions for the asymptotic variances of our test statistics and their estimation. Monte Carlo simulations suggest that the generalized Moran I tests introduced in this paper have the proper size and can provide substantial improvement in robustness when the researcher faces uncertainty about the specification of the network topology.