  A graph $H$ is common if the limit as $n\to\infty$ of the minimum density of
monochromatic labelled copies of $H$ in an edge colouring of $K_n$ with red and
blue is attained by a sequence of quasirandom colourings. We apply an
information-theoretic approach to show that certain graphs obtained from odd
cycles and paths via gluing operations are common. In fact, for every pair
$(H_1,H_2)$ of such graphs, there exists $p\in(0,1)$ such that an appropriate
linear combination of red copies of $H_1$ and blue copies of $H_2$ is minimized
by a quasirandom colouring in which $p\binom{n}{2}$ edges are red; such a pair
$(H_1,H_2)$ is said to be $(p,1-p)$-common. Our approach exploits a
strengthening of the common graph property for odd cycles that was recently
proved using Schur convexity. We also exhibit a $(p,1-p)$-common pair
$(H_1,H_2)$ such that $H_2$ is uncommon.
