Supporting Online Material Flavor network and the principles of food pairing by Yong-Yeol Ahn, Sebastian E. Ahnert, James P. Bagrow, Albert-Laszl´ o´ Barabasi´ Table of Contents S1 Materials and methods2 S1.1 Flavor network .................................... 2 S1.1.1 Ingredient-compounds bipartite network................... 2 S1.1.2 Incompleteness of data and the third edition................. 3 S1.1.3 Extracting the backbone ........................... 5 S1.1.4 Sociological bias ............................... 6 S1.2 Recipes ........................................ 6 S1.2.1 Size of recipes................................. 7 S1.2.2 Frequency of recipes ............................. 10 S1.3 Number of shared compounds ............................ 10 S1.4 Shared compounds hypothesis ............................ 11 S1.4.1 Null models.................................. 11 S1.4.2 Ingredient contributions............................ 13 List of Figures S1 Full ingredient network................................ 2 S2 Degree distribution of flavor network......................... 3 S3 Comparing the third and fifth edition of Fenaroli’s.................. 4 S4 Backbone ....................................... 5 S5 Potential biases .................................... 6 S6 Coherency of datasets................................. 8 S7 Number of ingredients per recipe........................... 9 S8 The distribution of duplicated recipes......................... 10 S9 Measures ....................................... 11 S10 Null models...................................... 12 S11 Shared compounds and usage............................. 13 List of Tables S1 Statistics of 3rd and 5th editions ........................... 3 S2 Recipe dataset..................................... 7 S3 Coherence of cuisines................................. 8 S4 Each cuisine’s average number of ingredients per recipe............... 9 S5 Top contributors in North American and East Asian cuisines ............ 15 1 S1 Materials and methods S1.1 Flavor network S1.1.1 Ingredient-compounds bipartite network The starting point of our research is Fenaroli’s handbook of flavor ingredients (fifth edition [1]), which offers a systematic list of flavor compounds and their natural occurrences (food ingredients). Two post-processing steps were necessary to make the dataset appropriate for our research: (A) In many cases, the book lists the essential oil or extract instead of the ingredient itself. Since these are physically extracted from the original ingredient, we associated the flavor compounds in the oils and extracts with the original ingredient. (B) Another post-processing step is including the flavor compounds of a more general ingredient into a more specific ingredient. For instance, the flavor compounds in ‘meat’ can be safely assumed to also be in ‘beef’ or ‘pork’. ‘Roasted beef’ contains all flavor compounds of ‘beef’ and ‘meat’. The ingredient-compound association extracted from [1] forms a bipartite network. As the name suggests, a bipartite network consists of two types of nodes, with connections only between nodes of different types. Well known examples of bipartite networks include collaboration net- works of scientists [2] (with scientists and publications as nodes) and actors [3] (with actors and films as nodes), or the human disease network [4] which connects health disorders and disease genes. In the particular bipartite network we study here, the two types of nodes are food ingredi- ents and flavor compounds, and a connection signifies that an ingredient contains a compound. The full network contains 1,107 chemical compounds and 1,531 ingredients, but only 381 ingredients appear in recipes, together containing 1,021 compounds (see Fig. S1). We project this network into a weighted network between ingredients only [5,6,7,8]. The weight of each edge wi j is the number of compounds shared between the two nodes (ingredients) i and j, so that the relationship between the M × M weighted adjacency matrix wi j and the N × M bipartite adjacency Figure S1: The full flavor network. The size of a node indicates average prevalence, and the thickness of a link represents the number of shared compounds. All edges are drawn. It is impossible to observe indi- vidual connections or any modular structure. 2 3rd eds. 5th eds. # of ingredients 916 1507 # of compounds 629 1107 # of edges in I-C network 6672 36781 Table S1: The basic statistics on two different datasets. The 5th Edition of Fenaroli’s handbook contains much more information than the third edition. matrix aik (for ingredient i and compound k) is given by: N wi j = ∑ aika jk (S1) k=1 The degree distributions of ingredients and compounds are shown in Fig. S2. S1.1.2 Incompleteness of data and the third edition The situation encountered here is similar to the one encountered in systems biology: we do not have a complete database of all protein, regulatory and metabolic interactions that are present in the cell. In fact, the existing protein interaction data covers less than 10% of all protein interactions estimated to be present in the human cell [9]. To test the robustness of our results against the incompleteness of data, we have performed 103 103 102 102 102 ) ) i c 101 N(k) N(k N(k 101 101 100 100 100 100 101 102 103 100 101 102 103 100 101 102 103 Ingredient degree, ki Compound degree, kc Degree in ingredient network, k 104 104 104 103 103 103 102 102 102 ) (cumulative) ) (cumulative) i c 101 101 101 N(k) (cumulative) N(k N(k 100 100 100 100 101 102 103 100 101 102 103 100 101 102 103 Ingredient degree, ki Compound degree, kc Degree in ingredient network, k Figure S2: Degree distributions of the flavor network. Degree distribution of ingredients in the ingredient-compound network, degree distribution of flavor compounds in the ingredient-compound network, and degree distribution of the (projected) ingredient network, from left to right. Top: degree distribution. Bottom: complementary cumulative distribution. The line and the exponent value in the leftmost figure at the bottom is purely for visual guide. 3 0.3 14 55.7 0.25 12 0.2 10 8 0.15 s 6 Z N ∆ 0.1 4 2 0.05 0 0 -2 -0.05 -4 North Western Latin Southern East North Western Latin Southern East American European American European Asian American European American European Asian 1.8 14 45.5 1.6 1.4 12 1.2 10 1 8 s 0.8 6 Z N 0.6 ∆ 4 0.4 2 0.2 0 0 -0.2 -2 -0.4 -4 North Western Latin Southern East North Western Latin Southern East American European American European Asian American European American European Asian Figure S3: Comparing the third and fifth edition of Fenaroli’s to see if incomplete data impacts our conclusions. The much sparser data of the 3rd edition (Top) shows a very similar trend to that of the 5th edition (Bottom, repeated from main text Fig. 3). Given the huge difference between the two editions (Table S1), this further supports that the observed patterns are robust. 4 Plant derivatives Plant Plants Vegetables leek vinegar rutabaga parsnip sesame oil sesame turnip cassava olive oil olive green bell pepper tomato juice coconut oil coconut black tea black tea bell pepper mustard carrot soy sauce soy Nuts and seeds and Nuts porcini green tea green zucchini vegetable oil vegetable cucumber peppermint oil peppermint jasmine tea jasmine lettuce soybean oil soybean maple syrup maple lima bean celery oil celery bean coffee shiitake roasted onion cocoa black bean peanut oil peanut pumpkin horseradish asparagus wood spirit wood mushroom cacao smoke brussels sprout cane molasses cane scallion sunflower oil sunflower onion endive beech rapeseed potato orange peel orange yam laurel yeast garlic lemon peel lemon tomato mandarin peel mandarin palm cauliflower leaf root cabbage capsicum annuum capsicum wood vegetable kohlrabi sauerkraut rhubarb roasted sesame seed sesame roasted roasted peanut roasted celery roasted hazelnut roasted roasted nut roasted squash coconut pea pistachio soybean peanut chickpea baked potato roasted pecan roasted walnut beet roasted almond roasted chicory pecan potato chip cashew chive nut kale kidney bean lentil broccoli seed radish hazelnut watercress sesame seed sesame artichoke mung bean almond red kidney bean oatmeal caviar Cereal cereal fish rice herring wheat salmon fatty fish haddock wheat bread wheat white bread white scallop buckwheat cod rye flour rye salmon roe egg noodle egg catfish Seafoods malt mussel oat smoked fish prawn corn grit corn bread shrimp crab katsuobushi popcorn shellfish rice bran rice corn oyster tunasmoked salmon rye bread rye seaweed barley lobster brown rice brown octopus squid whole grain wheat flour wheat grain whole sturgeon caviar macaroni clam crayfish corn flake corn lavender turkey tulip orange flower meat flower rose smoked sausage smoked bergamot geranium liver gardenia chamomile pork violet Flowers chicken liver chicken mutton pork liver pork beef pear brandy gin chicken grape brandy Meats rum roasted beef roasted sake beef broth beef cabernet sauvignon wine port wine lamb whiskey frankfurter chicken broth chicken cider cognac veal wine ouzo boiled pork boiled fried chicken fried beef liver beef brandy ham cherry brandy grilled beef grilled apple brandy pork sausage pork armagnac blackberry brandy cured pork cured bacon sherry wine beer champagne wine anise white wine drinks Alcoholic pepper red wine sherry vanilla mace coriander honey nutmeg lard cinnamon egg clove bone oil tamarind caraway galanga cayenne blue cheese turmeric butter cardamom tabasco pepper tabasco parmesan cheese sour milk cumin yogurtbutterfat