  Highly-entangled multi-photon graph states are a crucial resource in photonic
quantum computation and communication. Yet, the lack of photon-photon
interactions makes the construction of such graph states especially
challenging. Typically, these states are produced through probabilistic
single-photon sources and linear-optics entangling operations that require
indistinguishable photons. The resulting inefficiency of these methods
necessitates a large overhead in the number of sources and operations, creating
a major bottleneck in the photonic approach. Here, we show how harnessing
single-atom-based photonic operations can enable deterministic generation of
photonic graph states, while also lifting the requirement for photon
indistinguishability. To this end, we introduce a multi-gate quantum node
comprised of a single atom in a W-type level scheme coupled to an optical
resonator. This configuration provides a versatile toolbox for generating graph
states, allowing the operation of two fundamental photon-atom gates, as well as
the deterministic generation of single photons. We investigate the
implementation of this setup with a $^{87}$Rb atom and evaluate its performance
through numerical simulations.
