In this paper we model relations between chords by minimal transport and we investigate different types of dependencies within chord sequences. For this purpose we use the “System & Contrast” (S&C) model, designed for the description of music segments at the phrase scale, to infer non-sequential structures called chord progression graphs (CPG). Minimal transport is defined as the shortest displacement of notes, in semitones, between a pair of chords. The paper present three algorithms to find CPGs for chords sequences: one is sequential, and two others are based on the S&C model. The three methods are compared using the perplexity as an efficiency measure. The experiments on a corpus of 45 segments taken from songs of multiple genres, indicate that optimization processes based on the S&C model outperform the sequential model with a decrease in perplexity over 1.0.