Pitching Wedges

I don't play golf. But there is a long tradition of bankers playing golf that is memorialized in the famous 3-6-3 rule: bankers pay 3% interest on deposits, lend at 6% interest, and are out on the golf course by 3 PM.

So while this banking-themed post about the the World Bank Major Contract Award Network may seem be named after a type of golf club that is descended from the niblick, I'm actually going to just keep doing my job of selling everybody on the advantages of BioFabric "edge wedges".

This week, I'll focus in on a single edge wedge for one country, Niger, which I picked because it gives a manageably-sized high-resolution image, and has examples of each type of node I want to talk about. The small-scale version is below, and there is a high-resolution version available in the BioFabric gallery:

Click on picture to enlarge

As I outlined in a previous post, most of the contracts in the network are between a borrower country and suppliers who are exclusive to that country. So I created a custom layout that tucks those exclusive supplier nodes into the node rows right under the appropriate borrower country row. And of those exclusive suppliers, most are usually from the same country, but there are also some from other countries. Finally, for each country, there are some suppliers whose also have contracts with other borrower countries. Those nodes are not tucked in under a particular borrower country, but are at the very bottom of the network.

So, the nodes for each country are organized as follows:

1. Suppliers from that country who only have contracts with that country, ordered by number of contracts.
2. Suppliers from other countries who only have contracts with that country, ordered by number of contracts.

Those are exclusive links whose node lines do not extend beyond the wedge for the country. At the bottom of the network, we have:

• Suppliers from any country who have contracts with more than one country, ordered by total number of all contracts across all countries.

A close look at the Niger example above shows this arrangement in detail. Start by noticing how the regular gridding of the edges allows you to use the slope changes of the edge wedge to get distinct, and meaningful, visual clues as to what types of suppliers you are looking at. For example, the 45-degree slope regions are where you will find all the suppliers with only one contract. The parts of the wedge where the slope is shallower are where you will find the contracts for multi-contract vendors. 

So, for Niger, we have the following (looking at the high-resolution version from the Gallery may make this easier to follow):

There are two Niger-based suppliers with five contracts, and these appear in the very upper left, where the edge wedge slope is shallowest. Moving right and down, the wedge slope gets steeper, and we soon encounter a run of 22 suppliers with two contracts, followed by the prominent 45-degree section of Niger-based suppliers with only one contract. Note that within suppliers with the same number of contracts, the nodes are ordered alphabetically. (The sharp-eyed viewer will also note here that I had problems getting the correct encoding of the non-ASCII character set; this bug needs to be addressed.) The next prominent feature is the start of another shallow-sloped region of the wedge representing the foreign suppliers having multiple contracts with Niger (and only Niger), followed by the 45-degree slope region of foreign suppliers to Niger with one and only one contract in the network.

That marks the end of the suppliers in the network who only have contracts with Niger. The rest of the Niger contracts are with suppliers who have contracts with more than one country. Note that the node ordering here is based upon the global number of contracts for each supplier, and so the edge wedge slope is not smooth. We can see that the biggest "global player" with a Niger contract is UNICEF (not really surprising), with three contracts, but there are other suppliers lower down with more Niger contracts, though fewer global contracts overall. Note that in the subgraph view shown above, these nodes are tucked right in with the others, though they are distinct due to their long node lines. In the main view, they are at the bottom, with the long edges from each borrower forming sort of an umbilical cord for each. My last blog post about this network talked about how subgraph views are minimized using this sort of compression.

Click on image to enlarge

With this new understanding of how each borrower edge wedge is organized, you can download the BioFabric .bif file, uncompress it, load it up into BioFabric, and start exploring World Bank Major Contract Awards.  Note how BioFabric's ability to explicitly order nodes and edges permits the data to be presented in a completely organized fashion, despite having over 44,213 nodes and 66,021 edges. Also, note that this is actually a multigraph, i.e. there are multiple edges between nodes, and while adjacency matrices can be highly ordered, they have issues with showing multigraphs.

There should be one more post forthcoming to wrap up this discussion, but I'm also busy thinking about fun new D3-based demos. Stay tuned to see what's next.