Crystals arise as a result of the breaking of a spatial translation symmetry. Similarly, periodically-driven systems host non-equilibrium states when discrete symmetries in time are broken. These exotic phases are referred to as time crystals and are the focus of this work. We introduce a novel method to describe, characterize and explore the physical phenomena related to this new phase of matter using tools common in graph theory. We present for the first time the visualization of the time crystal order, explained in terms of clustering nodes. Our strategy provides a whole new framework to study the properties of such systems and to propose new paths from where to envisage prospective applications. Within this scope we study in detail the melting process of a 2T Discrete Time Crystal (2T-DTC) and describe it in terms of the evolution of the associated graph structure. In that perspective, networks evolving via a preferential attachment mechanism arise, suggesting that time crystals are ideal candidates to simulate complex quantum networks.
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