Mahogany wood stain can vary in depth, but in general it is a burgundy or dark red color with undertones of brown within the red. This is considered to be a warm-colored wood, so it would be best paired with warm paint colors and decor items. On the lighter side of the spectrum, ivory and cream are ideal. Contrast works well with this dark wood finish, so you can go for lighter colors in walls and decor.
Walnut wood comes in a variety of shades, but they all share the same characteristic. Walnut is a brown color with yellow undertones. This also places it within the warm color group. Walnut is a medium-brown color, not too light or dark. This gives it versatility when combining it with wall colors and decor. With this wood, you can go either lighter or darker with paint colors or decor items without any problem.
Although both of these woods are considered warm tones, that doesn't mean they can't be mixed with cooler tones, as long as a few simple rules are followed. White of course, goes with just about everything and will look very nice when paired against mahogany. For a darker color, green is a very good contrasting color for mahogany. With walnut wood, use the yellow undertones as your guide, and seek out a contrasting color such as blue. This keeps the colors friendly to the eye while giving you more variety.
Another consideration is the color of the room's wood trim or other pieces of furniture. Mixing and matching can create a discordant note in the room. Go for contrasts to cancel this out. For example, for light maple furniture or trim, choose mahogany wood. For darker brown woods, go with walnut to create the contrast. You can mix woods, but one must be darker or lighter than the other for the best effect.