Both approaches shed many doubts on the existence of relevant communities in the WTN, whether endogenously emerging or exogenously defined: the results show that the WTN is increasingly connected and PTAs (or other factors) do not split countries into significantly defined cohesive groups because of the presence of strong inter‐group connections keeping the system together. Some “weak” communities emerge, but the countries involved are generally not much more connected among them than with the rest of the world, so that they do not form truly privileged or exclusive relationships. Put it differently, in international trade globalization seems to prevail over regionalization or preferentiality, in spite of the high heterogenity of the countries.

First, we look for communities in the WTN in the period between 1962 and 2008, allowing the presence of preferential trade patterns to emerge endogenously from the world trade dataset, and we compare different methodologies to search for communities in networks, introducing also a measure of their significance, in order to verify the robustness of the results that we obtain. All the different methods applied here base the search for a community on the identification of a group of countries sharing a disproportionate amount of trade among them when compared with that they have with the rest of the world. The second type of analysis, instead, starts from exogenously defined clusters based on the existing PTAs, and aims to assess their significance as communities within the WTN structure.

In order to analyze the impact of PTAs on the structure of world trade, we look for the possible existence of communities within the WTN. Searching for communities in the WTN requires to examine the matrix of all the existing trade links, considering the world trading system as a whole, rather than assessing preferential trade on a bilateral basis. The possible effects of trade creation and trade diversion are therefore fully taken into account, considering the existing interdependencies for all countries. If the signed agreements significantly affect the geographical pattern of trade flows, by increasing trade between members and possibly by reducing trade with non‐members, community structures should emerge in the WTN. In fact, in general terms, a significant network community is a set of nodes with strong internal connections, much stronger than those with the remaining nodes of the network (Newman, 2006 ; Fortunato, 2010 ). What defines a community in this context are strong, above‐average commercial ties (relative to the rest of the world) rather than imposed partitions of the network, or common individual characteristics of the nodes. Community analysis applied to the WTN should then discover – without pre‐imposing any preferential link or structure – groups of countries with privileged relationships, originated by geographical vicinity, common language or religion, traditional partnerships, and of course preferential trade agreements, if they indeed do affect trade patterns. Instead, in a “globalized” or “multilateral” world, with no exclusive PTAs, we do not expect communities to be significant, as countries can be connected through trade to nearly any country in the world with similar ease.

Network analysis has been used to examine the formation of PTAs by Goyal and Joshi ( 2006 ) and Furusawa and Konishi ( 2007 ). In particular, Furusawa and Konishi ( 2007 ) address the issue of PTAs as “building or stumbling blocs”, looking at whether PTA formation is a process that will eventually lead to a complete network (with all countries linked to each other through preferential agreements) achieving global free trade. In this paper instead, we don't look at the process of creation of preferential trade linkages, but we analyze empirically the structure of the trade network to better understand how preferentiality (as opposed to randomness) in choosing trade partners impacts on the overall world trade network, and whether it leads to an open connected system rather than a sum of closed blocs.

In this paper, we address these issues using a different methodological approach, the network analysis of international trade flows. Among the many real‐world networks studied in the literature, the World Trade Network (WTN) received increasing attention in the last decade because of a number of interesting features (see De Benedictis and Tajoli ( 2011 )). It is quite natural to represent international transactions among countries as a network, where countries are the nodes and the connecting edges are the international trade flows between them, giving rise to an intricate system of exchanges affecting all the countries. The specific economic motivations driving international trade flows shape this network, that consequently displays characteristics that are relevant for their economic implications, as well as for the network analysis in itself.

The second issue deals with the possibility that PTAs give rise to isolated groups of countries, highly integrated among them, but separated from the rest of the world (i.e., possible “stumbling blocs” on the way to multilateralism, according to Bhagwati( 1991 )), and considers how PTA formation interacts with global trade (e.g., Westhoff et al., 1994 ; Ornelas, 2005 ; Saggi and Yildiz, 2010 ). This issue was addressed empirically less often in econometric models (e.g., Fukao et al., 2003 ; Magee, 2008 ), and mainly by building measures of regionalization of trade patterns, but all the proposed indices have potential drawbacks (De Lombaerde et al., 2011 ), leaving open the discussion on the effects of PTAs.

The decision of a group of countries to selectively lower or eliminate tariffs (and possibly other trade barriers) against imports from group's members, forming a Preferential Trade Agreement (PTA) has been discussed in trade policy debates for a long time. 1 Many works in the international trade literature show the increasing trend of preferential trade agreements since the 1990s, but there is no conclusive evidence on the actual effects of these treaties (Pomfret, 2007 ; Baier and Bergstrand, 2007 ). In the literature, among the many still open issues, there is very little agreement on two points in particular: the actual impact of PTAs on the trade flows between members, and the possible distortion produced on trade flows with non‐members. The first of these points has been addressed in the empirical literature relying mainly on the gravity model framework, 2 but this approach raises a number of concerns, especially because of the likely endogeneity of PTAs (Baier and Bergstrand, 2004 ; Baier et al., 2008 ; Wolf and Ritschl, 2011 ).

So far, very few studies analyzed communities, or clustering, within the WTN (Reyes et al., 2009 ; Barigozzi et al., 2011 ), possibly because of the many open issues still existing in the methodologies for community analysis, making the intepretation of the results quite problematic (Fortunato, 2010 ). A direct reference to PTAs when looking for communities in the WTN is made by Reyes et al. ( 2009 ), using as a benchmark the groups of countries that signed regional trade agreements, finding that over time the formation of communities follows an irregular pattern. The above‐mentioned studies define and detect communities in the WTN in distinct ways, but in all cases the main problem is that it is difficult to assess the significance of the partitions that emerge. This is the specific issue we address in what follows.

A problem in assessing the extent of preferentiality is that both theoretical and empirical recent work in international trade emphasizes that PTA membership should be treated as an endogenous choice, thereby making it difficult to isolate is own impact: Chen and Joshi ( 2010 ) and Baier et al. ( 2014 ) highlight the role of countries' interdependencies when analyzing PTAs. But it is not straightforward to deal empirically with this point, and a relatively small numbers of works do it explicitely (Magee, 2003 ; Egger et al., 2011 ). The community analysis performed on the WTN, by allowing the existence of countries' blocs to emerge endogenously, can address directly this issue, providing additional insights on the effects of PTAs on trade.

The eagerness to form PTAs orginated a large body of literature trying to understand the causes and the effects of this phenomenon. 3 At the basis of the interest both for economists and policy‐makers are the potentially important welfare implications of preferential agreements, which can be positive or negative, as discussed since Viner ( 1950 ). Most concerns on the increasing number of PTAs are related to the possibility that such agreements might distort patterns of trade by granting selective preferential treatment, thereby affecting the choices of trading partners (e.g., Bagwell and Staiger , 1997 ; Bond et al., 2004 ). In spite of many modeling differences, most works agree in showing that the potential negative welfare effects depend on the trade diversion and the terms‐of‐trade distortions that can be created by such arrangements (Krueger ( 1999 )). 4 Therefore, the extent of the actual “preferentiality” is a relevant issue.

The number of signed trade agreements increased very rapidly since the 1990s, and in 2014 over 350 such agreements were in force. Currently, all countries of the world are members of at least one trade agreement, with the only exception of Mongolia. According to the World Trade Organization (WTO, 2011 ), the value of trade between members of PTAs has grown faster than the world average in the past decades, increasing the share of PTA trade to world trade from 18% in 1990 to 35% in 2008. This remarkable coverage in terms of countries and its increase in time, however, overstates the extent of trade that actually takes place on a preferential basis. The number and scope of PTAs in fact is not fully conveying the effectiveness of these agreements in promoting trade among its members and, potentially, in diverting trade to non‐members. What matters most is the actual preferential reduction in tariffs and other trade barriers put forth by a PTA, and in many ways, the multiplication of PTAs reduces the exclusivity of a trade agreement, possibily watering down its effects.

In our sample, the total value of world imports increases from about 126 billion in 1962 to 15760 billion in 2008 (all amounts in U.S. dollars). The value of imports in our dataset represents approximately 95 per cent of total world imports in 2008 and slightly lower amounts in the previous years. 6 Not only the trade value but also the number of edges L registers a remarkable increase, passing from 7870 in 1962 to 21123 in 2008. The average in‐strengh of each node also increases correspondingly, but average values in this network are not especially relevant, as nodes and edges (in our case, countries and trade flows) are very heterogeneous.

A network is strongly connected if, for every pair ( i , j ) of distinct nodes, there exists an oriented path from i to j (e.g., Barrat et al., 2008 ). If the network is not connected, the set of nodes can be partitioned in components having, without loss of generality, N 1 ≥ N 2 ≥ … ≥ N m > 0 nodes, respectively ( ). Each component is a maximally strongly connected sub‐network (i.e., it is strongly connected and it is not part of a larger connected sub‐network). In our study, given the increase in international trade and in the number of trading partners for most countries, we will find that the largest component is actually a giant component , i.e., it has a dimension N 1 which has the same order of magnitude as N and, on the other hand, it is much larger than all the other components. Network components can be identified by means of standard algorithms of graph analysis. 5 In 1962, the strongly connected component includes 145 countries, and it keeps slowly increasing until 1985 when it jumps to 165. From 1995 onward, the giant component is composed of 180–182 countries, including the new countries born from the dismantling of the former Soviet bloc. In the analysis of the following section we will consider the giant component only.

Being the network directed, for each node i we distinguish between the in‐degree , the out‐degree , and the total degree , and we denote the average degree by . Analogously, we define the in‐, out‐, and total strength of node i as , , and , respectively, and the total weight of the network edges as .

The main topological properties observed by past analysis of the WTN are confirmed by this dataset, indicating that this network is disassortative (countries with few trade links tend to be connected to countries with a large number of links), with a high clustering coefficient (the trade partners of a given country are often trade partners themselves), and a number of small‐world properties (the average distance in terms of steps required to move from one node to another is small) (Serrano and Boguñá, 2005 ; Garlaschelli and Loffredo, 2005 ; Fagiolo et al., 2008 ). These properties are accompanied by (and partially arise from) the high heterogeneity of countries as traders, the diversity of geographical distances, and the complex structure of trade costs (Abbate et al., 2012 ). The evolution of the WTN over time is slow, but it is in line with the so‐called ‘globalization’ process, showing an increasing connectivity between nodes.

We use directed aggregate flows received by an importing country from any given exporting country (import data are generally more reliable and complete than exports), measuring the value in U.S. dollars at current prices. Here we are not concerned with the change in prices over time, as we do not make any time series analysis, but we consider the existence of communities in each year separately.

Data for our analysis come from the Direction of Trade Statistics published by the International Monetary Fund (IMF) and from the dataset made available by the Center for International Data at UC Davis, constructed from United Nations trade data by Feenstra et al. ( 2005 ), known as NBER‐UN Trade Data. We use annual bilateral imports for the years 1962, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005 and 2008 (in the paper we mostly display results for the first and last year of our sample, but the full, detailed set of results is available from the authors). A number of important events affected the patterns of world trade in the period considered: the end of colonial links, changes in the exchange rate regime, removal of many barriers to trade, increasing role of emerging countries in the international markets, and – as mentioned – a rising trend in the number of PTAs signed. Our observation period stops before the outbreak of the financial crisis affected international trade, which was still growing by 15% in value in 2008 before the dramatic drop recorded in 2009.

The WTN is here modeled as a directed, weighted network composed of N nodes corresponding to countries ( is the set of nodes) and L edges connecting countries, representing the trade flows among them. We denote by W = [ w ij ] the N × N weight matrix , where w ij ≥ 0 is the value of the trade flow from country i to country j . The connectivity matrix A = [ a ij ] is the N × N matrix where a ij = 1 if w ij > 0, i.e., if there exists the edge i → j , and a ij = 0 otherwise.

4. Communities in the World Trade Network

Consider now a directed, weighted, strongly connected network (or, if not connected, its giant component). Roughly speaking, a subset is called a community if the total weight of the edges internal to is much larger than that of the edges connecting to the rest of the network. In other words, community analysis looks for non‐random distributions of links between nodes, generating groups of nodes more tightly connected than the network average. In our WTN, a community arises if a subset of countries is trading relatively more (in a sense specified below) among them than with the rest of the world. This can occur for a number of reasons, but it is the effect that we expect to observe if a PTA is indeed promoting trade among its members, and trade within the PTA is indeed preferred to trade with the rest of the world, being more economically convenient. The advantage of using network community analysis is that there is no need to define ex‐ante the countries' groups, but the data structure itself will reveal them, if any. At the same time, the internal cohesion (or “preferentiality”) of these groups and their relevance can be measured taking simultaneously into account the strength of all the bilateral linkages within the group and outside the group, and their structure. In fact, the measures used to assess the significance of candidate communities are influenced not only by relative weight of internal versus external links of the community itself, but also by the relative relevance of the links of outside countries with community members, thereby capturing the possible role of trade diversion.

The community analysis of a given network with nodes consists therefore in finding the “best” partition (i.e., and for all h, k), according to some criteria (for simplicity, we do not consider possibly overlapping communities), namely the “best” grouping of countries that are close trade partners. Despite a huge amount of contributions in the network analysis literature (Fortunato, 2010), there is not consensus, however, on formal criteria for defining communities and for testing their significance. This is why we will use three different approaches to analyze communities in the WTN.

4.1. Modularity optimization Finding the partition that maximizes a quality index called modularity is by far the most popular method for finding communities in a given network. Originally proposed by Newman and coauthors (Newman and Girvan, 2004; Newman, 2006), this approach has found plenty of applications in diverse areas and has been extended in many directions. In the case of a directed and weighted network, the modularity Q associated to the partition is given by (1) which is the fraction of network weight internal to communities, minus the expected value of such fraction in a random network that has in common the in‐ and out‐strengths with the original one. Thus Q is large (i.e., it tends to 1, due to normalization) when the weight density internal to the sets (the communities) is large with respect to a random distribution of weights. Although the best partition (i.e., the one with Q = Q max ) cannot be found by exhaustive search even in rather small networks, for computational reasons, many efficient algorithms are available for obtaining a presumably “close to optimal” solution (Fortunato, 2010). We use the aggregative, hierarchical method devised by Blondel et al. (2008), which is considered very effective both in terms of Q max (i.e., in the capability of finding a partition with high modularity) and in computational requirements (Lancichinetti and Fortunato, 2009). The results of modularity optimization for all the years of our WTN dataset are in Table 1.7 In 1962 we obtain q = 4 communities with Q max = 0.225. The communities count 55, 44, and 42 countries, plus a very small community formed by only 4 countries. The largest communities essentially coincide with most of Europe and Africa, America, and Asia plus Oceania, respectively. This last community also includes UK and Ireland, still strongly linked to Commonwealth countries. From 1970 onward, the results show q = 3 with a similar grouping of countries (possibly with the exception of African countries, that tend to become more scattered across communities), and with UK and Ireland shifting to the European community, following their membership of the EEC in 1973. In this case, we see in the change of the community composition the possible effect of joining a PTA. Table 1. World Trade Network statistics in the 1962–2008 period, and the results of the max‐modularity community analysis. N: number of countries of the giant component; : average number of import partner countries; : average import value (million US dollars); Q max : max modularity; # comm.: number of communities, and number of countries for each community (The composition of each community is available from the authors on request) year N Q max # comm. 1962 145 54.2 870 0.225 4 [55,44,42,4] 1965 145 64.4 1197 0.223 4 [48,43,40,14] 1970 150 74.1 1949 0.244 3 [51,50,49] 1975 151 80.8 5528 0.238 3 [75,40,36] 1980 151 76.9 12322 0.232 3 [75,42,34] 1985 165 69.2 11383 0.282 3 [70,64,31] 1990 163 78.7 20330 0.260 3 [74,70,19] 1995 182 92.7 26315 0.281 6 [77,73,18,8,4,2] 2000 180 106.7 34432 0.290 3 [76,61,43] 2005 181 113.6 56024 0.294 3 [70,65,46] 2008 181 116.7 87056 0.296 3 [68,66,47] The number of communities temporarily increases in 1995, when trade flows for the new countries formed by the dismantling of the Soviet bloc start to be recorded, and indeed one of the communities is formed essentially by this group. Over time, the strong ties between these countries loosen up, as they appear no longer as a separate group, but mostly in the large Europe‐based community. In 2008 the communities contain 68, 66, and 47 countries, but the largest cluster is now associated to Asia/Oceania, confirming the rapidly increasing role of Asia in international trade. This clustering by continents is very much in line with the large body of literature showing that geographical proximity still matters for international trade and for the formation of trading blocs (e.g., Egger, 2008).8 A slightly larger modularity appears over time, reaching Q max = 0.296 in 2008, but this cannot be immediately seen as an increase in the relevance of our communities, as max modularity generally grows if the size of the graph increases. The problem we face now is the significance of the obtained network partitions. Maximizing the modularity obviously yields some “best” partition, but this does not imply that the network is actually structured in significant clusters. In our analysis, what emerges in most cases is a partition of the WTN into three (almost continental) blocs, which is the number that many observers expected to emerge “naturally”, but that was also seen as a welfare‐minimizing situation (Krugman, 1991). This could be a worrisome conclusion, but in fact what really matters for the welfare effects is the extent of intra‐bloc preferences (Frankel et al., 1998). If the three blocs are scarcely significant in terms of relevance of intra‐bloc trade with respect to inter‐bloc trade, welfare implications would be very different. This is why assessing the significance of the partitions is relevant. Although a large value of Q max , per se, should reveal that the network has a modular organization (as it measures a kind of “dissimilarity” between the network and its randomizations), a large value of Q max can even be obtained in random (i.e., Erdős‐Rényi) networks, which instead are expected to have no community structure by construction (Reichardt and Bornholdt, 2006). In addition, the values of Q max we obtain can hardly be considered to be large (compare, e.g., with the results reported by Newman (2006)). So, finding the partition that maximizes Q by no means concludes the community analysis of the network (Fortunato, 2010). For undirected, unweighed networks, some methods have been proposed for complementing the max‐modularity approach with a test of statistical significance. These methods, however, have some features that make their use problematic in our case. No straightforward extensions exist in the case of weighted, directed networks, for which the definition of randomized models and of suitable perturbation schemes is absolutely not trivial (see Piccardi et al. (2010) for some proposals). For these reasons, in the next sections we will move to completely different approaches for testing the existence and significance of communities in the WTN.

4.2. Cluster analysis Standard data clustering is aimed at organizing objects into “homogeneous groups”, trying to maximize at the same time the intra‐group similarity and the inter‐group dissimilarity. This needs defining a suitable distance among data. When we move to graph clustering, i.e., grouping the nodes of a network, which distance should be used is by no means obvious. We adopt the notion of similarity/distance among nodes proposed in Piccardi (2011), which is based on random walks. An N‐state Markov chain can straightforwardly be associated to the N‐node network9 by row‐normalizing the weight matrix W, i.e., by letting the transition probability from i to j equal to (2) The resulting transition matrix P = [p ij ] is a stochastic (or Markov) matrix, i.e., 0 ≤ p ij ≤ 1 for all i, j, and for all i. It is important to note that modeling the WTN by 2 corresponds to moving from absolute to relative trade values, since the flow from i to j is now normalized by the total export flow from country i. This allows to control for countries' different economic weight, and the consequence is that communities, if any, will not necessarily be composed of groups of countries related by large trading, but instead by countries with privileged partnership, namely whose trading is important in relative terms. As mentioned, this can be due to different factors, but certainly it should arise in presence of trade agreements that promote trade between members more than trade with non‐members because they give rise to a preferential treatment. Since we expect such communities to be composed of a mixture of large and small economies (Whalley, 1998; WTO, 2011), the use of relative trade values appears to be more appropriate, as absolute measures would a priori obscure the position of medium‐small countries. In defining a distance among nodes, we describe the global behaviour of a large number of walkers (a “fleet”) started from each node i, and we propose a similarity σ ij between nodes (i, j) defined by (3) Then the distance d ij = d ji between nodes (i, j) is defined by complementing the similarity and normalizing the results between 0 and 1: (4) The rationale underlying the definition of σ ij and d ij is to assign nodes (i, j) a large similarity if a numerous fleet of random walkers started in i makes a large number of visits to j (and viceversa) within a sufficiently small time horizon T.10 The notion of community induced by this metric, therefore, is that of a subnetwork where a random walker has a large probability of circulating for quite a long time, before eventually leaving to reach another group. Then a standard hierarchical, aggregative cluster analysis (e.g., Everitt et al., 2011) is used to explore the possible existence of communities. More precisely, a binary cluster tree (dendrogram) is computed by initially defining N groups each containing a single node, and then by iteratively linking the two groups with minimal distance. The dendrograms obtained for the WTN in 1962, 1980, and 2008 (i.e., the two extremes of the time window of our dataset, plus an intermediate year) are displayed in Fig. 1 (the full set of dendrograms with the indication of the countries is available from the authors). In the dendrograms, each vertical line corresponds to a node (a country). Horizontal lines (“links”) connect two groups of nodes, and the height of the link (as read on the y‐axis) is the distance between the two groups. Figure 1 Open in figure viewerPowerPoint Three dendrograms obtained by the hierarchical cluster analysis. Vertical lines correspond to countries. Horizontal lines (“links”) connect two groups of nodes, and the height of the link (as read on the y‐axis) is the distance between the two groups. The absence of long vertical segments denotes weak clusterization A clear, visual indication of a clusterized network structure would be the existence of long vertical segments or, equivalently, of links (i.e., horizontal segments) whose height is largely different from the heights of the links below them. In fact, this situation arises when the distance between the two groups joined by the link is much larger than the distance among the nodes forming the two groups – this exactly means that there are clusters in the network. The situation appears to be markedly different in the WTNs' dendrograms: no long vertical segment is shown and only few distinct groups appear, and they are mostly composed of few countries. Moreover, there seems to be no significant structural differences through the years, possibly with a diminishing visual distance between groups over time. In all years, some expected patterns can be observed: United States and Canada form one of the closest pairs; France is strongly connected to some of its former colonies; Germany is close to other European countries. Some of these links are very large both in absolute and in relative terms (e.g., between US and Canada), others are important in relative terms (e.g., over one third of the imports of New Caledonia come from France). Often very small countries are connected to much larger ones, confirming the disassortativity already observed in the WTN (Fagiolo et al., 2008). These links tend to be small in absolute terms, given the small economic size of the countries, but they are very important in relative terms, as they show a strong preference for a given partner. As pointed out above, the visual analysis of the dendrograms leads us to claim that the WTN, through the years, does not display a significant community structure.11 In summary, the results of the cluster analysis (although based on the visual evidence only) denote the absence of a strong evidence of the existence of a significant community structure in the WTN. Together with the small modularity level (Sec. 4.1), this is a further clue of a mild community structure of the WTN.

4.3. Persistence probabilities The final search on the existence of significant communities in the WTN is performed by extracting other quantitative indicators, namely the persistence probabilities of the communities. Starting from the N‐state network, a given partition induces a q‐state meta‐network, where communities becomes meta‐nodes. At this scale, the dynamics of a random walker can be described by a q‐state lumped Markov chain (Kemeny and Snell (1976)) with q × q stochastic matrix U.12 Under appropriate assumptions, the entry u cd of U is the probability that the random walker is at time (t + 1) in any of the nodes of community d, provided it is at time t in any of the nodes of community c. We define persistence probability of the community c the diagonal term u cc of U. Large values of u cc are expected for significant communities. In fact, the expected escape time from is τ c = (1 − u cc )−1: the walker will spend long time within the same community if the weights of the internal edges are comparatively large with respect to those pointing outside. The analysis of the persistence probabilities induced on a network by a given partition has recently been proved to be an effective tool for testing the existence and significance of communities (Piccardi, 2011). For directed networks, the persistence probability u cc turns out to be equal to: (5) where π i is the stationary state probability of node i (which satisfies π = πP, e.g., Meyer (2000)), and is the aggregate over community . Recalling that, in our WTN model, , we see that u cc is a convex combination (i.e., a weighted average) of the relative trade flows that the nodes of direct within the community. Notice that the coefficients of the convex combination are proportional to π i , which is a well‐known measure of centrality (i.e., importance) of node i (e.g. Newman, 2010). From 5, it straightforwardly follows that we obtain u cc ≥ α, for given 0 ≤ α ≤ 1, when all countries of direct at least the fraction α of their export within . However, we may have u cc ≥ α even if for some countries i, provided that these countries are those with low centrality. The measure of cohesion of a community provided in 5 is therefore based on the proportion of trade flows directed within the community (as opposed to the flows directed outside), , similarly to other standard measures of regionalization of trade flows. But differently from the traditional indices, through π i it takes explicitely into account the structure of the whole WTN, how the nodes (countries) belonging to the community interact with it, and the relevance of their outside connections for the structure of the community. We compute the persistence probabilities u cc , c = 1, 2, … , q, of the WTNs in the 1962–2008 period for the partition corresponding to the maximum modularity (Sec. 4.1): the results are in Fig. 2. If we individually analyze each single community, we discover that most of them turn out to be scarcely significant, as revealed by the small persistence probability. Indeed, let us define a community as meaningful if, for example, u cc ≥ 0.5: as discussed above, roughly speaking this means that members of community prefer to trade with other members of the same community at least half of the times. It is a very mild requirement: nonetheless, none of the partitions obtained from 1962 to 2000 fulfills it with all communities, whereas the requirement is met, although with a small slack, in 2005 and 2008, providing a clear indication that the WTN had over time a very mild clusterized structure. Figure 2 Open in figure viewerPowerPoint The persistence probabilities of the World Trade Network from 1962 to 2008. For each year, the circles denote the persistence probabilities of the q communities obtained via modularity optimization (vertical straight lines are for visual aid only). None of the partitions from 1962 to 2000 has all persistence probablities larger than 0.5 (a baseline requirement of significance), whereas this takes place, although with a small slack, in 2005 and 2008. Overall, this denotes a very mild clusterized structure of the WTN over time Yet, some important information is conveyed by the analysis of Fig. 2. Even if, in most instances, the partition of the WTN is scarcely significant as a whole, we notice that there is in each case (at least) one community with rather large persistence probability, both in absolute terms, and comparatively with respect to most of the other u cc 's. It turns out that it is a large community which always includes the entire set of European countries, plus a number of minor non‐European partners (partially varying from year to year), mainly from North Africa, Near East, and the Asian republics of the former USSR. Up to 1995, there is also another large community with high persistence probability, which includes the entire North America and most of Central and South America, plus China, Australia and many others. Since 2000, however, the community partition dictated by the max‐modularity suggests a different arrangement, with North and South America in a community and China and Australia in another one. Notably, both these new communities have a definitely smaller persistence probabilities than before, denoting less exclusive intra‐community partnerships. The evidence emerging from this analysis is partially in line with what can be expected looking at the existence of trade agreements between countries. Most European countries form the European Union (EU), the oldest and deeper custom union in the world, and the persistence of their ties is confirmed by the data. But this analysis also suggests that the EU is not a group of countries separated from to the rest of the world: indeed the observed community includes non‐EU members, and the not‐too‐high persistence probability suggests that trade links with other countries are also important (in 2008, over one third of the European Union imports were coming from non‐EU countries). The reported evidence also captures the new active role of China, which became a major player in many areas of the world, less dependent from the US market. Overall, we can conclude that, as well as the other methods above presented, the evaluation of the persistence probabilities confirms the absence of a strong clusterized structure in the WTN, when considered as a whole. However, the capability of the persistence probabilities of assessing the quality of each single community, differently from the other tools of analysis, puts forward the existence of some significant cluster of countries with privileged intra‐community partnerships.