2066 Y.L,D.Zhu/Physica A388(2009)2061-2071 a10° b 10 10 10 102 a 10 10 口Space L Space L o Space P o Space P 10 10 44 10° 101 10 10° 10 10 10 s C d 2000 103 1500 10 0 1000 00 0 10 ■Space L o Space P oSpace P 500 88 ■Space L 10° 0 500 1000 1500 2000 10 10 102 103 Fig.4.(a)Cumulative probability distributions of weight in two spaces.(b)Cumulative probability distributions of undirected strength in two spaces.(c) Linear relation between in-strength and out-strength in two spaces.(d)Correlations between strength and degree in two spaces.The slopes both equal to 1.3 approximately indicating nonlinear relationships in the spaces L and P. 2.5 a C(K) b ·C(K 口Space L 10° △C(K) o Space P 。cm(K 2.0 1.5 1.0 0 Ba 10 0.5 100 10 102 10 10 102 K 个 Fig.5.(a)Clustering coefficients.C(k)under two spaces both exhibit nontrivial behavior with decay curves as functions of degree k.And weighted versions of clustering coefficient are larger than unweighted clustering coefficient,indicating high traffic edges between interconnected vertices.(b)Rich-club coefficient.With Pran(k)>1 the worldwide maritime transportation network shows a rich-club ordering under both the space L and P. behavior with a decay curve as a function of degree k,signaling a hierarchy structure in which low degrees belong generally to well interconnected communities(high clustering coefficient),while hubs connect many vertices that are not directly connected(small clustering coefficient).2066 Y. Hu, D. Zhu / Physica A 388 (2009) 2061–2071 Fig. 4. (a) Cumulative probability distributions of weight in two spaces. (b) Cumulative probability distributions of undirected strength in two spaces. (c) Linear relation between in-strength and out-strength in two spaces. (d) Correlations between strength and degree in two spaces. The slopes both equal to 1.3 approximately indicating nonlinear relationships in the spaces L and P. Fig. 5. (a) Clustering coefficients. C(k) under two spaces both exhibit nontrivial behavior with decay curves as functions of degree k. And weighted versions of clustering coefficient are larger than unweighted clustering coefficient, indicating high traffic edges between interconnected vertices. (b) Rich-club coefficient. With ρran(k) > 1 the worldwide maritime transportation network shows a rich-club ordering under both the space L and P. behavior with a decay curve as a function of degree k, signaling a hierarchy structure in which low degrees belong generally to well interconnected communities (high clustering coefficient), while hubs connect many vertices that are not directly connected (small clustering coefficient)