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We show how the multivariable signature and Alexander polynomial of a colored link can be computed from a single symmetric matrix naturally defined from a colored link diagram. In the case of a single variable, it coincides with the matrix introduced by Kashaev in arXiv:1801.04632, which was recently proven to compute the Levine-Tristram signature and the Alexander polynomial of oriented links arXiv:2311.01923, arXiv:2310.16729. As a corollary, we obtain a multivariable extension of Kauffman's determinantal model of the Alexander polynomial, recovering a result of Zibrowius arXiv:1601.04915v1.
Cimasoni et al. (Mon,) studied this question.