Network Representation of the Product Space

-Maximum Spanning Tree
-Network Layout
-Node Sizes and Colors

We generated a network representation of the proximity matrix to help us develop intuition about its structure as well as to visualize and study the dynamics of countries on it. The matrix representing the product space has many small values which represent weak connections between products. That is why a network representation becomes an adequate way to layout the products, giving us a quick visual way to show the relevant links and to determine were countries are located and where they could be headed.

Maximum Spanning Tree (MST)

To include all products in our network we generated a "skeleton" for it: the Maximum Spanning Tree (MST). This is nothing more but the tree containing a sum of weights which is maximal. In other words, it is the set of N-1 links (N being the number of nodes) that connect all nodes in the network and maximizes the sum of the proximities in it.

We generated the MST by considering the strongest non-diagonal value of the proximity matrix and then considered the strongest link connected to that dyad. We then picked up the strongest link connecting a new node to our triad and continued adding links until all the nodes on the network were considered (Figure 4s).

Figure 1. Earliest version of the MST representing the "skeleton" of the product space.

We also wanted to consider the strongest links which are not necessarily in the MST. We did this by considering the MST plus all the links above a certain threshold. A suitable visualization was obtained by keeping all links with a proximity value of 0.55 or larger (Fig. 5s). This resulted in a network with 775 nodes and 1525 links. Lower proximity values gave rise to crowded network representations while higher values resulted in sparse networks. As a rule of thumb, a good network visualization can be achieved with an average degree equals to 4. This is when the number of links is twice the one of nodes, which is the case for the 0.55 threshold.

Figure 2. Representation of the product space based on the MST plus all links with a proximity above 0.55.

Network Layout

Good network visualization requires an appropriate layout. This is why we lay out the network using a force spring algorithm. Here nodes are represented as equally charged particles and links are assumed to be springs. The layout is determined by the relaxed positions.

Figure 3.Network representation of the product space layed out using a force spring algorithm.

The force spring layout is not the ultimate solution, but it brings us close to a good one. That is why we retouched the layout manually to avoid overlapping links and untangle dense clusters.

Node Sizes and Colors

An advantage of using a network representation is that we can simultaneously look at the structure of the space and other covariates. In our case we painted the network using the product classifications performed by Leamer[1], and made the size of the nodes proportional to the money moved by that particular industry or World Trade. To give a sense of the proximity of the links involved in our network representation we color coded them by using dark red and blue for strong links; and yellow and light blue for weaker ones.

Figure 4. Final version of the product space in which node size represents its world trade, node color shows its classification as proposed by Leamer and link color indicates a range in the proxmity values.

(1) E. Leamer , Sources of Comparative Advantage: Theory and Evidence (MIT Press, Cambridge MA, 1984).