Yong-Yeol Ahn, Sebastian E. Ahnert, James P. Bagrow and Albert-László Barabási mapped the flavor compounds shared by culinary ingredients:
A hypothesis, which over the past decade has received attention among some chefs and food scientists, states that ingredients sharing flavor compounds are more likely to taste well together than ingredients that do not. This food pairing hypothesis has been used to search for novel ingredient combinations and has prompted, for example, some contemporary restaurants to combine white chocolate and caviar, as they share trimethylamine and other flavor compounds, or chocolate and blue cheese that share at least 73 flavor compounds.
Their conclusion is that "while North American and Western European dishes tend to combine ingredients that share flavor compounds, East Asian cuisine avoids them." Hat tip to Nathan Yau, who notes that "Mushrooms and liver are on the edges, out on their lonesome." The whole map can be viewed here.