Networks of interacting Hawkes processes have emerged as useful models in neuroscience, geophysics, high frequency finance, and social network analysis. The Hawkes process is of fundamental importance, being a point process analog of an autoregression. Here we develop a fixed gain adaptive (aka online) distributed estimator for the parameters of a Hawkes process model. The stochastic intensity is modeled by a causal Laguerre basis expansion. The natural recursive structure of this basis is exploited to derive a new two time scale adaptive algorithm based on exponentially weighted least squares which preserves non-negativity constraints. Simulations illustrate the results.