Exponents for different products in OECD data set.

<p>The products in different industries coded by ISIC Rev.3 coding system for industries is shown. Industries of financial intermediation, business services, wholesale and retail trade, transport and storage, post and telecommunication, hotels and restaurants, and construction are ignored because their trades do not stand for goods flows. The last row shows the allometry of all industries as an integrated network.</p

Allometric exponents s of 1-digit classification products change with time.

<p>Allometric exponents s of 1-digit classification products change with time.</p

Distributions of Both Data Sets.

<p>The unit of is U.S.dollar.</p

Visualization of trade flow network for power generating equipment (upper) and fruit and vegetable (lower).

<p>We use different colors to distinguish nodes as importer (import is larger than its export) and exporter (export is larger than import). The size of node denotes the total volume of trade. In these two networks, only the backbones are shown as the main parts and all other un-important links are hidden as backgrounds. The backbone extracting method is according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098247#pone.0098247-Foti1" target="_blank">[35]</a>.</p

Exponents Distribution for All 4-digit SITC4 Product Categories.

<p>The stacked bar charts of different colors correspond to 1-digit SITC4 categories (left) and primary and manufacture classifications (right). For one specific 1-digit classification (say 0 for food and living animals), we can calculate the frequencies on each exponent intervals for all products with 0 prefix, then these frequencies as little bars are stacked on the tops of existing bars.</p

Exponents of 1-digit SITC4 categories in UN data set.

<p>The categories of 8 (Miscellaneous) and 9(Not classified) are ignored in this table, The last row shows the allometry of all products as an integrated network.</p

and for trees.

<p>In (a), the numbers inside the nodes are s and the numbers beside nodes are s. (b) is a flow network constructed according to (a), in which numbers represent flows. And dotted lines stand for dissipations.</p

The allometric scaling law between (in U.S. dollar) and (in U.S. dollar) of two networks are shown.

<p>The left figure shows a super-linear scaling law (with exponent larger than 1) for power generating product, while the right one shows a sub-linear scaling law (with exponent smaller than 1) for fruit and vegetable.</p

Two special spanning trees with minimum allometric exponent 1 (left, a star network) and maximum exponent 2 (right, a directed chain).

<p>Two special spanning trees with minimum allometric exponent 1 (left, a star network) and maximum exponent 2 (right, a directed chain).</p