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(a) Cumulative number of multilateral environmental agreements and cross-references; and number of new agreements each year, and different distributions of inward and outward citations as a function of the year in which cited and citing agreements were adopted, respectively. This network is symmetric, where the total number of inward citations equals the total number of outward citations. (b) Number of components, the size of the largest component, and the fraction of the largest component. (c) The average path length and the clustering coefficient of the multilateral environmental agreement network. 

(a) Cumulative number of multilateral environmental agreements and cross-references; and number of new agreements each year, and different distributions of inward and outward citations as a function of the year in which cited and citing agreements were adopted, respectively. This network is symmetric, where the total number of inward citations equals the total number of outward citations. (b) Number of components, the size of the largest component, and the fraction of the largest component. (c) The average path length and the clustering coefficient of the multilateral environmental agreement network. 

Contexts in source publication

Context 1
... from a single node in 1857 to 747 nodes with 1001 directed links (or 986 undirected links with multiple lines removed) in 2012. Fig. 1 shows eight graphical snapshots of the network taken at ten-year interval from 1941 to 2011 (and 2012). Increases in the cumulative number of agreements adopted and cross-references made since 1857 are shown in Fig. 2(a). Multilateral environmental agreements concluded before the mid-1940s often contained no cross- references. The average number of cross-references made (i.e., outward citations) per agreement grew rapidly after 1992, when the number of outward citations made each year clearly surpassed the number of agreements adopted each year (Fig. ...
Context 2
... shown in Fig. 2(a). Multilateral environmental agreements concluded before the mid-1940s often contained no cross- references. The average number of cross-references made (i.e., outward citations) per agreement grew rapidly after 1992, when the number of outward citations made each year clearly surpassed the number of agreements adopted each year (Fig. 2(a)). The total number of outward citations surpassed the total number of at 1941, 1951, 1961, 1971, 1981, 1991, 2001, and 2011 (and 2012) drawn using the layout algorithm of Fruchterman and Reingold (1991). The nodes of the largest components appear in blue. (For interpretation of the references to colour in this figure legend, the reader ...
Context 3
... structural changes could be quantified by a simple measure of the fraction of the largest component, which I plotted in Fig. 2(b). The fraction of the largest component was 1 with a single node in 1857. It continued to decrease, as more and more nodes with no links were inserted into the network, until the fraction reached the minimum at 0.056 (or 5.6 percent) in 1975. The network then consisted of 252 multilateral environmental agreements grouped into small and ...
Context 4
... density of local neighbourhoods, as measured by the clustering coefficient, began to increase in the 1980s (Fig. 2(c)). The clustering coefficient measures the fractions of potential connec- tions among network neighbours that are realized ( Watts and Strogatz, 1998). In other words, it quantifies how close the local neighbourhood of a multilateral environmental agreement is to being part of a 'clique', in which every agreement is connected to every ...
Context 5
... 2010). This system state transition happened around 1992 when new agreements brought a few shortcuts into the network. These shortcuts shrunk the size of the network while maintaining the level of local clustering. The average path length, which had consistently increased since 1857, started decreasing after reaching the peak of 6.53 in 1991 (Fig. 2(c)). The average path length is the average number of links that must be traversed in the shortest path between any two reachable pair of nodes, and it can be understood as a global measure of separation ( Watts, 1999Watts, , 2004). By 1992, the average path length dropped from 6.53 to 5.47 (Fig. 2(c)). The network diameter, which is the ...
Context 6
... after reaching the peak of 6.53 in 1991 (Fig. 2(c)). The average path length is the average number of links that must be traversed in the shortest path between any two reachable pair of nodes, and it can be understood as a global measure of separation ( Watts, 1999Watts, , 2004). By 1992, the average path length dropped from 6.53 to 5.47 (Fig. 2(c)). The network diameter, which is the maximum internode distance, also declined from 16 to 13 between 1991 and 1992. In 1992, the multilateral environmental agreement network started to become a small- world, and it has become smaller ever ...
Context 7
... multilateral environmental agreement system matured in the 2000s, when only a few agreements were concluded ( Fig. 2(a)). This recent trend can be attributed to what some called ''negotiation fatigue'' (Najam, 2000, p. 4048;see also Muñ oz et al., 2009). Anton (2012), for example, observed that, since 2002 and more noticeably 2005, the negotiation and adoption of multilateral environmental agreements have slowed. Struggling to meet current treaty ...
Context 8
... network has a single giant component of 421 multilateral environmental agreements and 870 citations, constituting 56 and 87 percent of the entire network, respectively (Fig. 1). The average path length is 4.70 (4.71 for the giant component) (Fig. 2(c)), and the two reachable agreements that are furthest apart are 12 steps away (Fig. 3). The clustering coefficient for the network is 0.43 (0.41 for the giant component) (Fig. 2(c)), which is orders of magnitude higher than 0.005 (AE0.002), the clustering coefficient of a corresponding Erdo ˝ s-Ré nyi random network which has the same ...
Context 9
... and 870 citations, constituting 56 and 87 percent of the entire network, respectively (Fig. 1). The average path length is 4.70 (4.71 for the giant component) (Fig. 2(c)), and the two reachable agreements that are furthest apart are 12 steps away (Fig. 3). The clustering coefficient for the network is 0.43 (0.41 for the giant component) (Fig. 2(c)), which is orders of magnitude higher than 0.005 (AE0.002), the clustering coefficient of a corresponding Erdo ˝ s-Ré nyi random network which has the same number of nodes and links (Erdo ˝ s and Ré nyi, ...
Context 10
... were distinct moments when highly cited agreements were adopted, such as the year 1982 that witnessed the conclusion of the United Nations Convention on the Law of the Sea (Fig. 2(a)). Time-dependent analysis indicated that these years (e.g., 1982) were followed by other years (e.g., 1992) in which the initially favoured set of agreements fell out of favour to be replaced by a different one, such as the Rio Conventions. A similar pattern could probably be observed at the level of norms. New norms such as ...
Context 11
... from a single node in 1857 to 747 nodes with 1001 directed links (or 986 undirected links with multiple lines removed) in 2012. Fig. 1 shows eight graphical snapshots of the network taken at ten-year interval from 1941 to 2011 (and 2012). Increases in the cumulative number of agreements adopted and cross-references made since 1857 are shown in Fig. 2(a). Multilateral environmental agreements concluded before the mid-1940s often contained no crossreferences. The average number of cross-references made (i.e., outward citations) per agreement grew rapidly after 1992, when the number of outward citations made each year clearly surpassed the number of agreements adopted each year (Fig. ...
Context 12
... shown in Fig. 2(a). Multilateral environmental agreements concluded before the mid-1940s often contained no crossreferences. The average number of cross-references made (i.e., outward citations) per agreement grew rapidly after 1992, when the number of outward citations made each year clearly surpassed the number of agreements adopted each year (Fig. 2(a)). The total number of outward citations surpassed the total number of at 1941, 1951, 1961, 1971, 1981, 1991, 2001, and 2011 (and 2012) drawn using the layout algorithm of Fruchterman and Reingold (1991). The nodes of the largest components appear in blue. (For interpretation of the references to colour in this figure legend, the reader ...
Context 13
... structural changes could be quantified by a simple measure of the fraction of the largest component, which I plotted in Fig. 2(b). The fraction of the largest component was 1 with a single node in 1857. It continued to decrease, as more and more nodes with no links were inserted into the network, until the fraction reached the minimum at 0.056 (or 5.6 percent) in 1975. The network then consisted of 252 multilateral environmental agreements grouped into small and ...
Context 14
... density of local neighbourhoods, as measured by the clustering coefficient, began to increase in the 1980s (Fig. 2(c)). The clustering coefficient measures the fractions of potential connections among network neighbours that are realized ( Watts and Strogatz, 1998). In other words, it quantifies how close the local neighbourhood of a multilateral environmental agreement is to being part of a 'clique', in which every agreement is connected to every ...
Context 15
... 2010). This system state transition happened around 1992 when new agreements brought a few shortcuts into the network. These shortcuts shrunk the size of the network while maintaining the level of local clustering. The average path length, which had consistently increased since 1857, started decreasing after reaching the peak of 6.53 in 1991 (Fig. 2(c)). The average path length is the average number of links that must be traversed in the shortest path between any two reachable pair of nodes, and it can be understood as a global measure of separation ( Watts, 1999Watts, , 2004). By 1992, the average path length dropped from 6.53 to 5.47 (Fig. 2(c)). The network diameter, which is the ...
Context 16
... after reaching the peak of 6.53 in 1991 (Fig. 2(c)). The average path length is the average number of links that must be traversed in the shortest path between any two reachable pair of nodes, and it can be understood as a global measure of separation ( Watts, 1999Watts, , 2004). By 1992, the average path length dropped from 6.53 to 5.47 (Fig. 2(c)). The network diameter, which is the maximum internode distance, also declined from 16 to 13 between 1991 and 1992. In 1992, the multilateral environmental agreement network started to become a smallworld, and it has become smaller ever ...
Context 17
... multilateral environmental agreement system matured in the 2000s, when only a few agreements were concluded ( Fig. 2(a)). This recent trend can be attributed to what some called ''negotiation fatigue'' (Najam, 2000, p. 4048;see also Muñ oz et al., 2009). Anton (2012), for example, observed that, since 2002 and more noticeably 2005, the negotiation and adoption of multilateral environmental agreements have slowed. Struggling to meet current treaty ...
Context 18
... network has a single giant component of 421 multilateral environmental agreements and 870 citations, constituting 56 and 87 percent of the entire network, respectively (Fig. 1). The average path length is 4.70 (4.71 for the giant component) (Fig. 2(c)), and the two reachable agreements that are furthest apart are 12 steps away (Fig. 3). The clustering coefficient for the network is 0.43 (0.41 for the giant component) (Fig. 2(c)), which is orders of magnitude higher than 0.005 (AE0.002), the clustering coefficient of a corresponding Erdo ˝ s-Ré nyi random network which has the same ...
Context 19
... and 870 citations, constituting 56 and 87 percent of the entire network, respectively (Fig. 1). The average path length is 4.70 (4.71 for the giant component) (Fig. 2(c)), and the two reachable agreements that are furthest apart are 12 steps away (Fig. 3). The clustering coefficient for the network is 0.43 (0.41 for the giant component) (Fig. 2(c)), which is orders of magnitude higher than 0.005 (AE0.002), the clustering coefficient of a corresponding Erdo ˝ s-Ré nyi random network which has the same number of nodes and links (Erdo ˝ s and Ré nyi, ...
Context 20
... were distinct moments when highly cited agreements were adopted, such as the year 1982 that witnessed the conclusion of the United Nations Convention on the Law of the Sea (Fig. 2(a)). Time-dependent analysis indicated that these years (e.g., 1982) were followed by other years (e.g., 1992) in which the initially favoured set of agreements fell out of favour to be replaced by a different one, such as the Rio Conventions. A similar pattern could probably be observed at the level of norms. New norms such as ...

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