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In this work, we investigate spreading processes that entail evolutionary adaptations on random graphs with tunable clustering and arbitrary degree distributions. We derive a mathematical framework that predicts the epidemic threshold and the probability of emergence as functions of the characteristics of the spreading object, the evolutionary pathways of the pathogen/misinformation, and the structure of the underlying network as given by the joint degree distribution of single-edges and triangles. To the best of our knowledge, our work is the first to jointly characterize the impact of clustering and evolution. We supplement our theoretical finding with numerical simulations and case studies, shedding light on how clustering can offer pathways for mutation, thereby altering the course of the epidemic.
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