Modeling complex contagion in networked systems is an important topic in network science, for which various models have been proposed, including the synergistic contagion model that incorporates coherent interference and the simplicial contagion model that involves high-order interactions. Although both models have demonstrated success in investigating complex contagions, their relationship in modeling complex contagions remains unclear. In this study, we compare the synergy and the simplest form of high-order interaction in the simplicial contagion model, known as the triangular one. We analytically show that the triangular interaction and the synergy can be bridged within complex contagions through the joint degree distribution of the network. Monte Carlo simulations are then conducted to compare simplicial and corresponding synergistic contagions on synthetic and real-world networks, the results of which highlight the consistency of these two different contagion processes and thus validate our analysis. Our study sheds light on the deep relationship between the synergy and high-order interactions and enhances our physical understanding of complex contagions in networked systems.

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