Fig. 3: Triple interactions reveal more associations with age than pairwise interactions.

The triple interaction (e.g., [A–C]) can be broken down into pairwise interactions ([A, B], [A, C], [B, C]) or their combined average. However, these decomposing pairwise interactions are not equivalent to the original triple interaction, as illustrated in A. To further illustrate this distinction, we examined how these interactions relate to brain development. B shows the strongest positive and negative triple network interactions across different infant ages. In C, we compare these interactions by presenting the associations derived from both the combined average of pairwise interactions and purely pairwise interactions, which are extracted from the z-score pairwise functional connectivity matrix. This comparison highlights the additional brain development information provided by triple interactions that is not captured by pairwise interactions alone. The colored dots represent age information, with colors from left to right corresponding to ages from 0 to 6 months.