Food and Complex Networks !

In this post we talk about Food network, “Food Pairing Hypothesis” and variants and invariants in food ingredient usage across different cuisine and in different times. Ingredient-flavor networks are bipartite networks describing the association of flavor compounds of food ingredients. This undirected graph consists of two different types of nodes: the ingredients used in the recipes and the flavor compounds that contributes to the flavor of each ingredients.

In the first part we will discuss whether there  are any general patterns that determine the ingredient combinations used in food today or principles that transcend individual tastes and recipes. In 2011, Yong-Yeol Ahn, Sebastian E. Ahnert, James P. Bagrow and Albert-László Barabási investigated the ingredient-flavor networks of North American, Latin American, Western European, Southern European and East Asian cuisines. Based on culinary repository epicurious.com,allrecipes.com and menupan.com, 56,498 recipes has been included in the survey. According to Ahn, in the total number of 56,498 recipes studied, 381 ingredients and 1021 flavor compounds were identified. Averagely each ingredients connect to 51 flavor compounds. It was found that in comparison with random pairing of ingredients and flavor compounds, North American cuisines tend to share more compounds while East Asian cuisines tend to share fewer compounds. It was also showed that this tendency was mostly generated by the frequently used ingredients in each cuisines.

Although many factors such as colors, texture, temperature, and sound play an important  role in food sensation palatability is largely determined by flavor, representing a group of sensations including odors , tastes, and freshness or pungency - all these are mainly due to the internal chemical compounds making them a natural starting point for a systematic search for principles that might underlie our choice of acceptable ingredient combinations.

Let us first describe the “Food Pairing Hypothesis” - 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. Here they have introduced a network-based approach to explore the impact of flavor compounds on ingredient combinations. Analyzing the data the authors built a bipartite network consisting of two different types of nodes: (i) 381 ingredients used in recipes throughout the world, and (ii) 1,021 flavor compounds that are known to contribute to the flavor of each of these ingredients. A projection of this bipartite network is the flavor network in which two nodes (ingredients) are connected if they share at least one flavor compound.

Following is the Ingredient - flavour network.

After taking the projection we have found the flavour flavour network

Following is The distribution of recipe size, capturing the number of ingredients per recipe, across the five cuisines explored in our study.

The following is the frequency-rank plot of ingredients across the five cuisines show an approximately invariant distribution

The previous image was an approximate visualization of the network, as the actual network has many nodes here we have clustered them for better visualization. Each node denotes an ingredient, the node color indicates food category, and node size reflects the ingredient prevalence in recipes. Two ingredients are connected if they share a significant number of flavor compounds, link thickness representing the number of shared compounds between the two ingredients.

This allows to model the food pairing hypothesis as a topological property: do we more frequently use ingredient pairs that are strongly linked in the flavor network or do we avoid them? The next figure (part D) indicates that North American and Western European cuisines exhibit a statistically significant tendency towards recipes whose ingredients share flavor compounds. By contrast, East Asian and Southern European cuisines avoid recipes whose ingredients share flavor compounds (see Figure D for the Z-score, capturing the statistical significance of ΔNs).

The systematic difference between the East Asian and the North American recipes is particularly clear if we inspect the P(Nrands) distribution of the randomized recipe dataset, compared to the observed number of shared compounds characterizing the two cuisines, Ns. This distribution reveals that North American dishes use far more compound-sharing pairs than expected by chance (Fig.E), and the East Asian dishes far fewer (Fig.F). Finally, we generalize the food pairing hypothesis by exploring if ingredient pairs sharing more compounds are more likely to be used in specific cuisines.

Schematic illustration of two ingredient pairs, the first sharing many more (A) and the second much fewer (B) compounds than expected if the flavor compounds were distributed randomly. (C,D) To test the validity of the food pairing hypothesis, we construct 10,000 random recipes and calculate ΔNs. We find that ingredient pairs in North American cuisines tend to share more compounds while East Asian cuisines tend to share fewer compounds than expected in a random recipe dataset. (E,F) The distributions P(Ns) for 10,000 randomized recipe datasets compared with the real values for East Asian and North American cuisine. Both cuisines exhibit significant p-values, as estimated using a z-test. (G,H) We enumerate every possible ingredient pair in each cuisine and show the fraction of pairs in recipes as a function of the number of shared compounds. To reduce noise, we only used data points calculated from more than 5 pairs. The p-values are calculated using a t-test. North American cuisine is biased towards pairs with more shared compounds while East Asian shows the opposite trend (see SI for details and results for other cuisines). Note that we used the full network, not the backbone shown in Fig. 2 to obtain these results. (I,J) The contribution and frequency of use for each ingredient in North American and East Asian cuisine. The size of the circles represents the relative prevalence . North American and East Asian cuisine shows the opposite trends. (K,L) If we remove the highly contributing ingredients sequentially (from the largest contribution in North American cuisine and from the smallest contribution in East Asian cuisine), the shared compounds effect quickly vanishes when we removed five (East Asian) to fifteen (North American) ingredients. C through H imply that all the recipes aim to pair ingredients together that share (North America) or do not share (East Asia) flavor compounds, or could we identify some compounds responsible for the bulk of the observed effect? We therefore measured the contribution χi (see Methods) of each ingredient to the shared compound effect in a given cuisine c, quantifying to what degree its presence affects the magnitude of ΔNs.

Here we discuss a little about the “Flavour Principle” - According to an empirical view known as “the flavor principle”  the differences between regional cuisines can be reduced to a few key ingredients with specific flavors: adding soy sauce to a dish almost automatically gives it an oriental taste because Asians use soy sauce widely in their food and other ethnic groups do not; by contrast paprika, onion, and lard is a signature of Hungarian cuisine.

In the next figure we organize the six most authentic single ingredients, ingredient pairs and triplets for North American and East Asian cuisines in a flavor pyramid.

Here (A,B) Flavor pyramids for North American and East Asian cuisines. Each flavor pyramid shows the six most authentic ingredients (i.e. those with the largest ), ingredient pairs (largest ), and ingredient triplets (largest ). The size of the nodes reflects the abundance of the ingredient in the recipes of the particular cuisine. Each color represents the category of the ingredient and link thickness indicates the number of shared compounds. (C) The six most authentic ingredients and ingredient pairs used in specific regional cuisine. Node color represents cuisine and the link weight reflects the relative prevalence     of the ingredient pair.

In another work we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural ‘founder effect’ produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes

For each cookery book database, we counted the number of recipes in which each ingredient appears. The ingredients were ordered according to descending frequency of usage. This allows the representation of the statistical hierarchy of ingredients in a cookery book by a frequency-rank plot, as introduced by Zipf. The next figure gives the frequency-rank plots for the Brazilian (1969 edn), British, French and medieval cookery books, showing a remarkable similarity in their statistical patterns. Time invariance is supported by the data next figure, which give the frequency-rank plots for the editions of the Brazilian cookery book. The structure of ingredient rankage in the Brazilian cookery book remained stable amidst the change from a regional to a more globalized food consumer profile that took place in the last 50 years. All these curves exhibit a power-law behaviour which can be well fitted by a Zipf–Mandelbrot law to capture finite size effects

(a) Cultural invariance. Frequency-rank plot for different cookery books: Pleyn Delit (circles), Dona Benta 1969 (squares), New Penguin (stars) and Larousse Gastronomique (triangles). (b) Temporal invariance. Frequency- rank plot for Dona Benta 1946 (squares), 1969 (lozenges) and 2004 (circles)

In another recent work, we collect a new data set of recipes from Medieval Europe before the Columbian Exchange and investigate the flavor pairing hypothesis historically. A strong determinant of the flavor of foods is the aromatic compounds that reach the olfactory system, either through the nose or through retro-olfaction. Humans are adept at detecting even trace amounts of these compounds and they have a great effect on hedonic perception. Chemically, flavor compounds come from groups such as acetals, acids, alcohols, aldehydes, esters, furans, hydrocarbons, ketones, lactones, and phenols. The primary calculation to understand the flavor pairing hypothesis is to compute the average number of shared flavor compounds among the ingredients in a recipe R. Let R be a set of nR different ingredients. Then the average number of shared compounds is

where Ci is the set of flavor compounds in ingredient i and Cj is the set of flavor compounds in ingredient j.

Medieval recipes were chosen for several reasons. One reason is that they have much historical interest. In fact, reading historical cookbooks as inspiration for new dishes. As we have discussed, we are interested in examining the effect of data sets with different properties, and thus we conduct empirical studies with two different flavor compound databases: VCF and Fenaroli.  They found the following trends in the dataset

For other results please refer to the reference. Now to end the post we can see that in our own country there is so much diversity of cuisines - whose underlying network is worth exploring !

Reference:

• https://www.youtube.com/v/qWAF9PgDg2c&start=271&end=381

• http://arxiv.org/abs/1111.6074  Flavour network and the principles of food pairing [Yong-Yeol Ahn, Sebastian E. Ahnert, James P. Bagrow, Albert-László Barabási]

• http://iopscience.iop.org/1367-2630/10/7/073020/pdf/1367-2630_10_7_073020.pdf   -- The non-equilibrium nature of culinary evolution [Osame Kinouchi, Rosa W Diez-Garcia, Adriano J Holanda, Pedro Zambianchi and Antonio C Roque]
• http://ssg.mit.edu/~krv/pubs/VarshneyVWM_ijcaiw2013.pdf Flavor Pairing in Medieval European Cuisine: A Study in Cooking with Dirty Data - [Kush R. Varshney, Lav R. Varshney, Jun Wang and Daniel Myers]