We propose Atomic Active Messages (AAM), a mechanism that accelerates irregular graph computations on both shared- and distributed-memory machines. The key idea behind AAM is that hardware transactional memory (HTM) can be used for simple and high performance processing of irregular structures in highly parallel environments. We illustrate techniques such as coarsening and coalescing that enable hardware transactions to achieve considerable speedups in graph processing. We conduct a detailed performance analysis of AAM on Intel Haswell and IBM Blue Gene/Q and we illustrate various performance tradeoff between different HTM parameters that impact the efficiency of graph processing. AAM can be used to implement abstractions offered by existing programming models and to improve the performance of graph analytics codes such as Graph500 or Galois.