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Various tensor models have been recently shown to have the same properties asthe celebrated Sachdev-Ye-Kitaev (SYK) model. In this paper we study in detailthe diagrammatics of two such SYK-like tensor models: the multi-orientable (MO)model which has an $U(N) \times O(N) \times U(N)$ symmetry and a quartic$O(N)^3$-invariant model whose interaction has the tetrahedral pattern. We showthat the Feynman graphs of the MO model can be seen as the Feynman graphs ofthe $O(N)^3$-invariant model which have an orientable jacket. We then present adiagrammatic toolbox to analyze the $O(N)^3$-invariant graphs. This toolboxallows for a simple strategy to identify all the graphs of a given order in the$1/N$ expansion. We apply it to the next-to-next-to-leading andnext-to-next-to-next-to-leading orders which are the graphs of degree $1$ and$3/2$ respectively.

Diagrammatics of the quartic $O(N)^3$-invariant Sachdev-Ye-Kitaev-like tensor model