The period-$c_2$ invariance conjecture for primitive log-divergent graphs

Let $G$ be a connected graph with at least three vertices, let $P(G)$ denote its period, and let $c_2(G)$ denote its $c_2$-invariant. Period-$c_2$ invariance conjecture. For two primitive log-divergent graphs $G_1$ and $G_2$,

$$P(G_1)=P(G_2)\quad\Longrightarrow\quad c_2(G_1)=c_2(G_2).$$

This conjecture says that the $c_2$-invariant is determined by the period. It is attributed in the source to K3phi4.