Main actors in the Cephalopod Global Trade Network: a graph theory analysis


 The global cephalopod trade is a multi-billion-dollar industry that involves fishing and captive breeding of a dozen species of high commercial value. It also contributes wholly or partly to the income and subsistence of thousands of families around the world. Despite its broad ecological, social, and economic importance, limited research has been conducted to describe the scope and scale of the global cephalopod trade. To date, there is no specific regulation, nor have tracking systems been implemented, to study the traceability of the global cephalopod trade at an international level. We provide, for the first time, a comprehensive description of the legal trade in cephalopods to understand who the key world players in the cephalopod seafood markets are. We analysed 20 years of records compiled by the United Nations COMTRADE database. The database contained 115,108 entries for squid and cuttlefish and 71,659 entries for octopus, including the product flow between traders (countries or territories) weighted by volume (kg) and monetary value (USD). Graph theoretic analysis was used to explore the emergent properties of this database through the analysis of different measures of centrality that provide insights on the key role of the traders in the network. Our findings show that most of the market movements between ca. 250 traders are led by three countries (China, Spain, and Japan), involving 11 clusters of traders based on the volume and value of cephalopod trade and number of transactions. The most important cluster, that dominates the cephalopod seafood market, is composed by 5 Asian countries (China, India, Republic of Korea, Thailand, and Vietnam), 2 European countries (the Netherlands and Spain) and the USA. This work identifies the traders that act as major exporters and/or importers, the modulators, intermediaries or accumulators, the best-connected traders, the principal flow routes and the weaknesses of the global cephalopod trade network. This network information is essential to advance towards a transparent and sustainable cephalopods world trade.


Introduction
Cephalopods account for around 2.5% of global sh production. Landings have increased in relative terms by 416% since 1961 to reach an all-time maximum of around 4 million tonnes in 2013, before dropping to around 3 million tonnes in 2019 (Fig. 1a). East Asia and South America, led by China and Peru, drive the increase in production, while Japan has halved its cephalopod production over the past 50 years 1,2 (Fig. 1b, 1c). Even with the clear global trend of declining cephalopod catches since 2013, their commercialisation in volume (tonnes) and monetary value (USA dollars, hereafter USD) has followed a steady increasing trend since the 1950s, by 6-fold in volume and 14-fold in USD. East Asia and South America (particularly Peru and Argentina, including Malvinas/Falkland Islands) have concentrated the highest production of volume in the last 20 years, staying in the same predominant position since the 80's (Fig. 1b, 1c). Regarding cephalopod market value, Asian (China, Japan, Thailand, Republic of Korea (South Korea), Vietnam, India), European (Spain, Italy), African (Morocco) and North American (the USA) countries hold the 10 most important shing eets in the world 2 .
Considering relevant stocks of squid and octopus, worldwide catches of short n squid (Illex spp., see family Ommastrephidae in Fig. 1a) fell from 850,000 tonnes in 2014 to 200,000 tonnes or less in recent years. Short n squid catches in the Malvinas/Falkland Islands had been low (43,400 t) in recent years and the year 2019 marked the third consecutive year of slow recovery of the South Patagonian stock after its extremely low abundance observed in 2016 3 . Non-favourable oceanographic conditions for stock migrations and intense activity of foreign shing eets (China, Japan, Republic of Korea, Taiwan, Spain) are key factors affecting the current abundance of the stock 3,4 . The United Kingdom's departure from the European Union (Brexit) in 2020 has also increased uncertainty within the cephalopod market because the structure and dynamic of the global squid trade are expected to be seriously altered. For example, squid producers and traders from the Malvinas/Falkland Islands may lose access to the highly relevant Spanish market. This would affect the pro tability of the Spanish shing eet based in the Port of Vigo, for which the Illex shery generates €200 million (c.a. USD$ 235 million) per year 5  To decipher the cephalopod trade network, it is important to understand both the key supplier dynamics and the main consumers of cephalopods over time. According to the Food and Agriculture Organization 2,8 , Eastern and Southeast Asian and Southern European countries or territories had the highest per capita supply of domestic cephalopods in 2013 (Fig. 2). In 2013, the Republic of Korea, Japan, Taiwan, and Spain had the highest availability of cephalopods for local consumption, all exceeding 10 g/capita/day (Fig. 2). Although the Republic of Korea and Japan dominate cephalopod consumption today, squid consumption in some Asian countries, such as Japan, has declined since the 1980s. Conversely, in Spain, consumption of all cephalopod groups has increased in line with imports (in volume) since the 1980s, although catches by the Spanish eet have gradually declined 2 .
Despite good knowledge on the current global state of cephalopod catches and consumption, vast information gaps exist about the major global players in the cephalopod seafood market. Faced with one of the world's greatest challenges -how to feed more than 9 billion people by 2050 in a context of climate change, economic and nancial uncertainty, and growing competition for natural resources -the international community made unprecedented commitments in September 2015 when UN Member States adopted the 2030 Agenda for Sustainable Development (UN SDG), namely UN SDG 14 (Life Below Water) 9 . As global sh stocks have been progressively over shed 2 , global cephalopod biomass has increased 10 ; however, there is evidence of overexploitation of some cephalopod species. To achieve the UN SDGs, complex interactions between the ecological abundance of commercial marine species and economic trends need to be fully understood. Ecological 10,11 and economic studies have focused on biomass and environmental changes in key cephalopod sheries (e.g., the Patagonian short n squid shery) 4 , while global patterns of cephalopod seafood markets are still unknown.
Global sheries and trade databases have been extensively analysed to extract the main harvesting, importing, and exporting traders (countries or territories); however, less effort has been devoted to understanding international cephalopod trade ows and their characteristics, despite their scale and scope. By addressing this knowledge gap, complex network methods have the potential to analyse the global trading system in a way that reveals many new topological and dynamic features of a network of interacting elements (e.g., stakeholders, enterprises, or countries). One relevant topic in the study of world trade is to explore the role of traders geographical entities, their in uences, and the situation they occupy in the network 12 . It has been observed that the forces of complex network links, called weights in graph theory, also provide promising properties, and can allow insights into the details of networks. In graph theory, a system of connected elements can be de ned as a "network", also called a "graph". Network elements are modelled as "vertices" or "nodes" in the graph and their connections or links are represented as "edges" or "arcs". In a trade network, the graph represents the network itself, with each trader being a vertex or node, and the probability of connection or ow of commodities between traders being the arcs or edges. Graph theory provides insights into the system properties and identi es critical nodes with high centrality (i.e., connected to many other traders) or clusters of well-connected nodes with high potential trade ow and acting as bridges between distant world regions. Centrality is a measure that indicates the relevance of a node in a network. It should measure the 4 P's -Prestige, Prominence, imPortance and Power 13 . Each node could be important from a different point of view depending on how that "relevance" is de ned. The study of centrality in graph theory is intended to identify the most important nodes in a graph given its topology.
The aim of this work is to apply graph theory to the global cephalopods trade network to identify the trading relationships between traders. We explored the cephalopod trade ow globally by using 20 years of records compiled by COMTRADE, the United Nations International Trade Statistics Database, freely accessible at https://comtrade.un.org/data/. The database used includes over 185,000 records, including the ow between traders weighted by volume (kg) and monetary value (USD). By exploring different measures of network centrality, we could assess emerging patterns in what we called the Cephalopod Global Trade Network (CGTN) to identify the most relevant actors for cephalopod global trade.

Methods
In this study, we compute measures of network analysis and apply network graph visualization tools to cephalopod shery trade ows to understand their nature and dynamics at a planetary level. Speci cally, we study the octopus, squid, and cuttle sh global trade networks where the extent of trade between a pair of traders can be treated as the link weight. Data was extracted for 252 countries or territories and 20 consecutive years (2000 -2019) from the UN COMTRADE database. Data extraction was done through the COMTRADE API using the package "comtradr" v.0.2.2 14 for the R language and environment for statistical computing version 4.0.3, released on 2020-10-10 15 . The COMTRADE API requires that searches for speci c commodities are done using commodity codes. Codes used for cephalopods are listed in Table 1.
Using these codes, we conducted queries on all imports and exports reported by any trader from 2000 to 2019. The output was a database having each transaction reported by trader organized in a timestamped (year) origin-destination format, followed by the quantity of the product traded in volume (kilograms) and the value of the transaction (USD). The traded products were identi ed as either fresh (live, fresh, or chilled product) or elaborated (frozen, dry, salted, in brine) for (1) octopus and for (2) cuttle sh and squid.
These two categories are prede ned in the COMTRADE database following the Harmonized System Nomenclature ("HS") and cannot be disaggregated by species or other taxonomic groups. The HS is an international customs terminology for the classi cation of goods that is currently applied by more than We used graph theory to establish sound theoretical connections between traders involved in the CGTN and analyse the emergent structure of the underlying network of trade connections. We rst constructed a directed graph weighted by monetary value (USD) or volume (kg). We considered these different measures to identify potential different patterns in the trade network driven by monetary or volume transactions of cephalopod products. Each node in the graph is identi ed as a country or territory involved in a trade transaction. However, since not all traders shared trade relationships, the number of nodes was always less than the 230 traders originally identi ed in the database.
The relationship between each pair of nodes was identi ed in the network with a link (edge) and the nature of the trade operation (export or import) is determined by the directionality of the link. Therefore, the directionality was denoted with an arrow pointing to the importing country or territory. Each edge in the graph was weighted by the total monetary value or volume involved in all transactions between two nodes over time. Therefore, the size of the nodes represents the relevance of the traders in the global trade network according to the sum of the weights of the edges, in monetary value or volume, owing from or to each trader (i.e., the node strength or the weighted degree of the nodes). The edges represent the ow of trade, the width of the edge represents the quantity of commodity traded between two nodes. Multi-annual data were normalised to indicate relevance rather than gross values. Finally, for a better understanding of the trade relations between the different countries and territories, the nodes were geolocated on a world map.
To identify emerging properties within the CGTN, we calculated different centrality measures considering trade links generated by aggregate gross export ows (in either monetary value or volume) calculated for the sum of all trades over the years. Centrality measures are useful to determine the relative importance of nodes and edges within the overall network 16 . In networks consisting of several nodes, some nodes play a decisive role in facilitating many network connections. Such nodes are central in network organization and are often identi ed by a range of metrics known as centrality measures. Here, we calculated 11 measures of centrality for the CGTN: Degree, In-degree, Out-degree, Strength, In-strength; Out-strength; Betweenness, Eigenvector centrality; Kleinberg's hub centrality score (hereafter Hub score); Kleinberg's authority centrality score (hereafter Authority score); and Page Rank. We selected these centrality measures as those metrics potentially useful in trade network studies. They are a product of a rst screening that included all existing measures of centrality, identi ed from a review of the existing literature. A full description of each centrality measure selected, its scope, and market interpretation, is provided in Table 2. Note that Degree of a node is the number of edges that arrive at that node. In a directed graph the degree is usually divided into the In-degree and the Out-degree (whose sum is the degree of the node). Out-strength and In-strength correspond to the weighted Out-degree and weighted Indegree of the node, respectively, and Strength (weighted Degree) corresponds to the sum of In-strength and Out-strength.
Hierarchical clustering of agglomerations using the Ward's clustering method was used to produce groups of traders that minimize within-group dispersion at each binary fusion. A priori statistical signi cance of the clusters was tested using the similarity pro le (permutations = 999, number of expected clusters = 1000) of the members of the identi ed density clusters.
All analyses were performed using the R language and environment for statistical computing 15 . Network graph analyses were performed using R package "igraph" v.1.2.5 17 . Hierarchical clustering analyses were performed using the package " ashClust" v.1.01-2 18 . Network visualisations were made with R packages:

Trends of cephalopods trade
Since 2000, trade in fresh octopus has been constantly dominated by the ow from China to Korea, followed by Vietnam to Japan, Portugal to Spain and Spain to Italy. However, there has been a marked decrease in the traded volume and monetary value over time, and it has been reduced by 50% in the top 5 trading traders.
Over the last 20 years, fresh octopus exports have been strongly dominated by China, followed by Spain, Vietnam, Portugal, and France, and recently by Morocco and Thailand. While Vietnam was the most important exporter in the rst period (2000)(2001)(2002)(2003)(2004)(2005), it has disappeared from the top 5 traders in the last ve years. Imports have been dominated by Korea, Italy, and Portugal, with no notable changes in the whole period. Regarding trade of processed octopus, the largest transactions have been performed from Morocco to Spain, Morocco to Japan, Mauritania to Japan (and more recently also to Spain) and China to Korea. Since 2000, exports of processed products have been dominated by Morocco, Mauritania, China, Spain, and Vietnam, while imports have been led by Japan, Spain, Italy, Korea, and the United The CGTN involves 220 traders (countries or territories) around the globe (Fig. 3). The remaining 32 traders either have no reported exports or were negligible (less than 500 kg in 20 years). The most important cluster of traders is composed by 8 countries that dominate the cephalopod global markets in Asia (China, India, Republic of Korea, Thailand, Vietnam), Europe (the Netherlands, Spain) and the USA.
The second most relevant cluster is composed by 11 traders involving 3 developed (Belgium, Canada, Denmark) and 8 developing countries (Argentina, Chile, Malaysia, Morocco, Philippines, Senegal, South Africa, UAE). Some of these traders have the most productive cephalopod sheries in the world (e.g., Patagonian short n squid in the Southwest Atlantic Ocean). 'Betweenness' identi es important actors facilitating ow through the network. For fresh octopus, the most relevant traders are Spain, France, and Italy, followed by Thailand, Portugal and the USA. Again, no major differences exist between the monetary value and volume networks. However, the ranking of traders changes when considering volume, as Italy replaces France in the second place, Indonesia adopts a more key role, and the most important bridge moves from Spain-Thailand to Spain-the USA (Fig. S1).

Octopus
Traders with a higher closeness have a high probability of exporting to the nearest neighbouring countries or territories; this measure also identi es important traders in a regional context. The traders with the highest closeness considering the monetary value and volume networks are China, Spain, Portugal, and Vietnam (Fig. S2). The Eigenvector reveals traders that are well connected in the network, identifying their area of in uence within the network (traders with which they are connected). In this case, there are differences between the monetary value and volume networks. The in uential nodes in the monetary value network are European traders including the Netherlands, Ireland, Belgium, and Romania. On the other hand, the in uential traders regarding the volume network are globally distributed, including Indonesia, Canada, Russia, Republic of Korea, the Netherlands, and Czech Republic (Fig. 5).
Traditionally, Indonesia has acted as a hub importing a large volume (kg) of fresh octopus from 37 traders (e.g., India, Philippines, Vietnam, Singapore, Slovenia) and redistributing it to over 200 traders. Other traders that act as worldwide hubs are Slovakia (Europe), Canada (North America), Peru (South America) and Kenya (Africa). Regarding monetary ow, Peru appears as the most important hub.
Although Peru is a large producer, it imports fresh octopus from Chile which it then markets to over 26 traders (Fig. S3).
Authority scores for the volume network reveal which traders have multiple import routes and strong preferential relationships with speci c buyer traders in the network (e.g., Czech Republic, Russia, Korea, Canada) (Fig. S4 top). For the monetary value network, Authority scores reveal which traders import from many sources then export to a few destinations while increasing the value of the product. Traders with high Authority scores for the monetary value network could be acting as regulatory actors of the selling price (e.g., Belgium, the USA, the Netherlands, Spain, Hong Kong, Brazil, Japan, Canada, Chile) (Fig. S4  bottom).

Elaborated octopus
The normalised strength reveals a diversi ed trade network for elaborated octopus products. Several relevant actors are distributed globally (e.g., Spain, Japan, Morocco, Mauritania, Italy, China, Republic of Korea, Vietnam, Portugal, the USA) and are developing different important routes (e.g., from Morocco to Spain; from Mauritania and Morocco to Japan; from Mauritania to Spain and from China and Vietnam to Korea). These routes show a common pattern: the origin is in developing countries or territories (that emerge as producers) while developed countries show a high and stable consumer demand. The network based on volume is highly similar to the monetary value network. However, Italy, China, Korea, Vietnam, and the USA reduce their importance compared to the top-ranked traders (i.e., Spain, Japan, and Morocco). The most important routes of the volume network are from China to Korea; Morocco to Spain; Morocco and Mauritania to Japan and Vietnam to Korea (Fig. S5).
The Betweenness measure highlights the role of Spain as a facilitating actor in the trade network of elaborated octopus, followed by Italy, China, and the USA. Similarly, the routes from Italy to Spain, and from Spain to China and the USA emerge as relevant in the network structure (Fig. 6). There are no major differences between the most central traders in this network and the volume-based one. Notably, the route between the USA and the Philippines is more important in the volume-based network (Fig. S6).
The most important traders according to the closeness measure for both the monetary value network and the volume-based network are Morocco, Mauritania, China, Vietnam, and Spain. These traders may place their commodities quickly and effectively in the network, in uencing the transactions of their closest partners (Fig. S7).
The eigenvector reveals the foremost importance of the Netherlands as a gateway for elaborated octopus to the European market, both in monetary value and volume (Fig. S8). Other European traders with a high eigenvector in the monetary value network are Malta, Lithuania, Cyprus and the United Kingdom. Elsewhere, China and Japan play a key role (Fig. S8 top). Central and Eastern European traders also have high eigenvector values in the volume-based network (e.g., Estonia, France, Lithuania, Luxembourg, Poland, Slovenia, Austria), highlighting a strong network of connections across the continent (Fig. S8 bottom).
The hub scores for monetary value and volume-based networks for elaborated octopus mostly highlight European traders as actors that buy from few sources and sell to several partners (Fig. S9). The Authority score again reveals the foremost importance of the Netherlands as a gateway to the European market, both in monetary value and volume. The Netherlands is a trader with many import routes that sells to few traders, mostly in Europe (Fig S10). The normalised strength revealed the importance of Spain, France, Italy, and India in the trade network of fresh squid and cuttle sh products, especially the route between east Asia and Spain (Fig. 7). The volume-based network (Fig. S11 bottom) is highly similar to the monetary value network.
For fresh squid and cuttle sh, Betweenness identi es Spain as leading the worldwide trade ow in both monetary value and volume networks, while Italy, France, India, China, and the USA are facilitators in terms of both monetary value and volume. However, in the volume-based network, the Netherlands and Myanmar stand out, forming a bridge between the European and Asian markets (Fig. 8).
According to the closeness centrality measure for monetary value and volume-based networks, India may be able to commercialize fresh commodities quickly and effectively among its trading partners (Fig. S12). To a lesser extent, this property is also observed for France, Spain, Yemen, and Morocco.
The Eigenvector score reveals a similar pattern to that emerging from the fresh octopus network, highlighting many quality links among European traders (i.e., relationships with other well-connected traders) in the volume-based network. In this network, the Netherlands is revealed as an important gateway to Europe. In Asia, Thailand takes this role. In the monetary value network, Peru stands out due to its strategy of sourcing only from Chile and redistributing to 26 traders around the world (Fig. S13).
Hub centrality highlights Peru in the monetary value network. This may be driven by its role as an accumulator of fresh commodities from Chile, and exporter to traders with a dominant position in cephalopod pricing (Fig. S14). Authority centrality highlights several traders around the world in the monetary value network: Thailand, Korea, Canada, Denmark, South Africa, Singapore, Chile, Australia, and Spain. In the volume-based network, the central traders are European, with Ireland and the Netherlands at the top, while the rest of the world is dominated by Singapore and Thailand (Fig. S15).

Elaborated squid and cuttle sh
The trade networks based in monetary value and volume for elaborated squid and cuttle sh emerge as global and complex, where several far distant traders have relevant roles in the import/export network (Fig. 9). Although the most important nodes in the volume-based network re ect important nodes in the monetary value network, the strengths of the links, i.e., the ow of value and volume, do not. For example, in the volume-based network, Peru exports the largest quantities of squid and cuttle sh to China (Fig. 9 bottom), but the ow of money for these transactions has lower importance ( Fig. 9 top).
The betweenness centrality metric (both monetary value and volume based) shows the importance of China, the USA, and Spain (followed by Italy, Korea, and Thailand) as facilitators in the processed goods trade network (Fig. S16). While the main bridges in volume transactions are between Italy and Spain, Spain and China, and China and the USA (Fig. S16 top), the main monetary bridges are from the USA to China, followed by the routes from Spain to the USA and from Italy to Spain (Fig. S16 bottom). That is, the key protagonists are the same, but they follow different directions.
Closeness centrality highlighted the main actors in a regional context (Fig. 10). In both the monetary value and volume-based networks, China, North and South Korea, India, Indonesia, Thailand, and Vietnam form a strong trade network for squid and cuttle sh processed in Asia. Key players include South America (Peru, Argentina, Chile, the Malvinas/Falkland Islands); the USA; the Mediterranean (Morocco, Spain); Africa (South Africa, Mauritania); and the West Paci c region (New Zealand, Japan) (Fig. 10).
The eigenvector centrality shows the most important international gateways for the monetary value and volume-based networks and their main destinations. For example, the Netherlands and neighbouring destination traders within Europe; Indonesia, Singapore, Korea and Japan on the Asian continent; or South Africa or the United Arab Emirates in the rest of the world (Fig. S17).
The combined hub score of the monetary value and volume-based networks identi es hubs and redistributors of elaborated squid and cuttle sh products around the world: Indonesia, Japan, Thailand, the Netherlands, Portugal, Poland, United Kingdom, and many other European traders (Fig. S18).

Discussion
Although trade involving cephalopods increased its contribution to the global seafood market in monetary terms (USD), as well as in volume, from 2000 to the mid-2010s, there has been limited research to describe the scope and scale of global trade in cephalopods. There is no speci c regulation, nor have monitoring systems been implemented, to study the traceability of cephalopods at the international level.
In European waters, the catch of cephalopods in large-scale sheries is virtually unregulated. Since they are often not the target species, cephalopod catches are only indirectly controlled, for example through restrictions on the types of shing gear that can be used and catch quotas set for non-cephalopod species. In artisanal cephalopod sheries, especially in southern Europe 21 , regulatory restrictions on shing activity are numerous, but few regulations are aimed at maintaining the status of cephalopod stocks, and these regulations are not always enforced, resulting in suspected high levels of illegal, unreported and unregulated (IUU) shing.
Sanctions on international trade agreements can be a persuasive tool to discourage unsustainable practices such as illegal, unreported, and unregulated (IUU) shing 22 26 . In this context, trade control is a powerful tool to regulate unsustainable practices of the largely unregulated cephalopod sheries. We provide the most comprehensive description of the legal trade in cephalopods to understand the routes and key world players i with a methodology that, systematically applied, could contribute to achieving transparency and traceability of cephalopod seafood markets.
In the context of global trade, the ability of a given trader to connect with other traders that demand products from it, thus creating a ow of goods, is often referred to as connectivity. Therefore, from an economic perspective, the main concern is the role of each trader and its in uence on the trade network, which is closer to the term "centrality" from a graph theory perspective. Many economic studies use wellknown centrality measures, but do not identify them as such 27 . In this study, we have identi ed the bestconnected traders according to different measures of centrality weighted by monetary value or volume.
The Eigenvector centrality measure reveals hubs in the trading network, such as Peru that imports squid and cuttle sh products from Chile and redistributes them to many traders. Another centrality measure, Betweenness, reveals the modulators that connect clusters of traders. Elimination of a modulator can fragment the trading network. For example, in the elaborated octopus trading network, Spain, Italy and China are key network modulators.
Our analysis reveals that traders with the highest import and export rates in many cases are not the most important gateways. In the case of fresh octopus, China and Korea were the largest capital players (highest strength), but the Netherlands is the trader that controlled world trade ow (highest eigenvector).
However, three European countries (Spain, Italy, and France), with the highest betweenness, played a critical role for connectivity at the international level. They acted as bridges between different communities of traders, and thus allow traders from different communities to be connected not only with their neighbours, but also with traders from other communities. The commercial routes for fresh octopus  Geography is important for developing countries to take part in cephalopod trade. Developing countries tend to trade with the hub that is geographically closest, with large rms tending to be involved in global production networks while small rms trade within the region 25  connections. In the other direction, there are traders, such as South Africa in the elaborated squid network, that act as aggregators, but in this case importing (enormous quantities in USD) from many different traders and then exporting to a few destinations (high Authority score).
All the above situations may be due to multiple or interrelated factors such as high GDP, foreign direct investment, the presence of trade agreements, economic complementarity, and historical and cultural ties that make a country or territory the most important trading partner for a single country or group of countries 27 . The ow of elaborated squid and cuttle sh in volume presents some interesting particularities that, as mentioned, could be affected by external factors. For example, the strong Malvinas/Falkland Islands-Spain relationship and, in the last decade, Peru-China. This scenario might change as Brexit-associated economic risks include the adoption of new taxes for cephalopod exports for Spanish shing vessels which have been operating in Malvinas/Falkland waters over the last three decades.
We identi ed the second most relevant cluster in the CGTN as being composed of eight developing countries (Argentina, Chile, Malaysia, Morocco, Philippines, Senegal, South Africa, UAE), some of which host the most productive cephalopod sheries in the world. Our results also identi ed that elaborated octopus products tend to move from developing to developed countries. These ndings re ect the global North's increasing importance as a net importer of natural resources from the South, showing a high specialization on a growing demand for cephalopods.
Simultaneously, these results also cause traders in the South to place greater economic importance on resource intensive primary sectors and taking on a greater environmental burden as a result 28 . Some developing countries have trade de cits due to exporting more sheries resources to developed countries than they import. There is ongoing debate about whether this is bene cial or detrimental to the exporting traders in terms of loss of access to the exported foods compared with increased purchasing power from income generated from those exports 29 . The ow of cephalopod products may contribute to food distribution equity by improving access to nutrient rich foods across countries or territories and socioeconomic groups 30 .
Nevertheless, a growing demand for sheries resources can lead to increased exploitation of stocks with implications for the environmental, social, and economic sustainability of sheries in developing countries where corruption and illegal shing practices are often the logical response to a lack of effective policy and regulatory frameworks 31,32 . Furthermore, the energy cost of transporting products through the complex trade links as well as the carbon sink prevented by the removal of cephalopods we have described from the oceans 33 , must also be considered in terms of resource use and carbon emissions.
Rising from 13% in 2000 to 16% at their peak in monetary terms between 2014 and 2016, and from 29% in volume terms in 2000 to 30% in 2014, cephalopods are one of the fastest growing products in terms of market share in the global seafood trade. However, in the last three years they have reached their lowest global seafood market share for the last two decades, at 5% in both monetary value and volume. On average, the price of fresh octopus was ca. 2.2 USD/kg in 2000, and by 2018, it had increased 5-fold to ca. 11.6 USD/kg. Similarly, but at a lower rate, the traded quantities of elaborated octopus have decreased in recent years and the monetary value of these transactions has increased. On average, the trade of elaborated products has increased from 2.6 USD/kg in 2000 to 10.2 USD/kg in 2019. These results suggest that trade for live, fresh, or chilled octopus is better positioned in the market, either due to growing consumer interest or to a shift towards healthier consumption habits. There is a growing interest among chefs and gastroscientists to promote novel uses of cephalopods to replace meat from land-animal production 34 .
The complexity of the trade ows we have described along with variations in (or lack of) labelling systems and o cial lists of seafood trade names in different countries or territories can make it di cult to accurately identify the origin of raw material used in cephalopod products, especially in processed preparations where potentially identi able anatomical features have been removed 35 . Lack of traceability measures creates opportunities for exploitation through product mislabelling or substitution with species of lower commercial value, as well as abusive practices such as the addition of water to arti cially increase product weight [35][36][37] . Mislabelling can have signi cant impacts on efforts to sustainably manage associated shers 38 . There are several ways of communicating to consumers about the environmental sustainability of seafood products and shing activities. This is mostly done through labelling, certi cation and ratings programs, in some cases also supported by guides for consumers, and most of them are operated by non-governmental organizations (NGOs). The most rigorous and credible The commercial routes of live, fresh, or chilled octopus have been strongly dominated by four trade ows concentrated in China and Southern Europe (i.e., China to Korea, Portugal to Spain and Spain to Italy and Portugal). Traders with a higher closeness have a high probability of exporting to the nearest neighbouring trading partners (not always geographically close), and it also identi es key traders in the regional context. The traders with the highest closeness are China, Spain, Portugal, and Vietnam. Wellconnected traders have a high ow of imports and exports with traders that also have a high ow of imports and exports; while traders that have multiple trade routes with strong relationships with buyer traders prefer them over other traders in the network.
These results suggest that trade in live, fresh, or chilled octopus is better positioned in the market, either due to growing consumer interest or a shift towards healthier consumption habits. The processed octopus is also principally traded from China to Korea. However, the routes are more diverse and variable over time, with important routes including Morocco to Spain, Italy and Japan, Mauritania to Japan, and Vietnam to Korea. Trade routes for fresh squid and cuttle sh have been highly concentrated by the largest monetary transactions from India to Spain, losing relevance in the last ve years, when the ow of capital has been greater between European traders (e.g., from Spain and France to Italy and from France to Spain).
Our ndings identify the traders that act as major trade actors, modulators, intermediaries, accumulators, the best connected, the ow routes and the possible weaknesses of the global cephalopod trade network. This work provides essential input to advance towards transparent and sustainable cephalopod world trade. Given the increasing scale and speed of the cephalopod industry activity, we conclude that the industry has truly global effects today.  Molluscs; cuttle sh and squid, whether in shell or not, includes ours, meals, and pellets of molluscs, t for human consumption, dried, salted, in brine, or smoked, cooked or not before or during the smoking process In-strength Barrat et al. 2004 In directed networks, the In-strength is the sum of inward link weights.
Traders with a high in-strength could act as important importers or hubs for the distribution of raw materials. High instrength could also be targeting traders acting as major consumers of products.
Out-strength Barrat et al. 2004 In directed networks, the Out-strength is the sum of outward link weights.
Traders with high out-strength may be acting as raw producers with high export ows. This may indicate the geographical origin of the commodities and essential habitats for the species. Out-strength can also indicate whether a trader is a major exporter of processed products.

Closeness
Freeman 1979 Closeness centrality indicates how long it will take for information from a given node to reach other nodes in the network.
Traders with a higher closeness have a high probability of exporting to the nearest neighbouring traders. These traders could be important in trade at regional or continental geographic scales.

Betweenness Freeman 1979
Betweenness centrality is a measure of the in uence of a node over the ow of information between every pair of nodes under the assumption that information primarily ows over the shortest paths between them. Imports and exports are important, but they are not the whole picture. Traders with high Betweenness centralities have been called "bottlenecks" or "bridges" and prevent network fragmentation. A trader that acts as a bridge between two well differentiated groups of traders usually has a high Betweenness.

Bonacich 1987
The Eigenvector centrality network metric takes into consideration not only how many connections a node has (i.e., its Degree or Strength), but also the centrality of the vertices that it is connected to.
It is a measure of a trader's in uence in the trade network. In general, a connection to a well-connected trader is more important than a connection to a poorly connected trader. Traders with high Eigenvector centralities have a high ow of imports and exports mainly with traders that also have a high ow of imports and exports.

Kleinberg 2000
The Hub score of a node shows how many highly informative nodes or authoritative nodes this node is pointing to.
High Hub scores may be associated with traders that import products from a few traders for export to several other traders. They may indicate those traders that act as collectors of raw products to be redistributed as such or processed before export.

Kleinberg 2000
The Authority score of a node is a measure of the amount of valuable information that this node holds.
High Authority scores may be associated with traders that import from many traders to export to a few others. It is interpreted similarly to the authority score. The approximate estimation of the importance of a trader is based on the number and quality (weight) of the links pointing to it. The most important traders are likely to import more products from other traders in the network.    node represents a trader, and each edge represents the export-import relationship between two traders.

Figures
The size and colour of the node represent the relative importance of the trader in the network in terms of its strength. The width and colour of the edge represents the relative importance of the relationship between two traders in terms of their edge strength.  Each node represents a trader, and each edge represents the relationship between two traders. The size and colour of the node represent the relative importance of the trader in the network in terms of its betweenness. The width and colour of the edge represents the relative importance of the relationship between two traders in terms of their edge betweenness. Global trade network for squid and cuttle sh live, fresh or chilled between 1 January 2000, and 31 December 2019 in monetary value (USD). The numbers correspond to the normalised strength for the monetary value. Each node represents a trader, and each edge represents the export-import relationship between two traders. The size and colour of the node represent the relative importance of the trader in the Page 28/30 network in terms of its strength. The width and colour of the edge represents the relative importance of the relationship between two traders in terms of their edge strength. Global trade network for squid and cuttle sh live, fresh or chilled between 1 January 2000, and 31 December 2019 in monetary value (USD) above, and mass (kg) below. The numbers correspond to the normalised betweenness for the monetary value (USD) and mass (kg) traded, respectively. Each node represents a trader, and each edge represents the relationship between two traders. The size and colour of the node represent the relative importance of the trader in the network in terms of its betweenness. The width and colour of the edge represents the relative importance of the relationship between two traders in terms of their edge betweenness. Global trade network for squid and cuttle sh elaborated between 1 January 2000, and 31 December 2019 in monetary value (USD) above, and mass (kg) below. The numbers correspond to the normalised strength for the monetary value (USD) and mass (kg) traded, respectively. Each node represents a trader, and each edge represents the export-import relationship between two traders. The size and colour of the node represent the relative importance of the trader in the network in terms of its strength. The width and colour of the edge represents the relative importance of the relationship between two traders in terms of their edge strength. in monetary value (USD) above, and mass (kg) below. The numbers correspond to the normalised closeness for the monetary value (USD) and mass (kg) traded, respectively. Each node represents a trader. The size and colour of the node represent the relative importance of the trader in the network in terms of its closeness.