Taxonomy of Studies on Interconnectedness, Accessible Data
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Taxonomy figure
This figure shows an organization branching chart of our taxonomy. It has three colors to demonstrate the different levels of distinction between studies. The type of approach is in blue, the type of analysis is in green, and output measures are in purple.
On the left, the top box is the blue "network approaches" box; this branches into green "direct" and "indirect (price data)" boxes. Still in the green analysis boxes, the "direct" box branches into "Interbank" and "CDS" boxes; the "indirect" box branches into "Granger Causality", "Portfolio Analysis", and "Variance decomposition boxes". All of these lower green boxes connect and branch into two purple output boxes: "Network measures" and "simulation results".
On the right, the top box is the blue "non-network approaches" box; this branches into green "PCA", "Regression", and "Default models" boxes. The "PCA" box connects to a purple "Absorption ratio/CRF" box; the "Regression" box connects to a purple "Co-movement Coefficient" box; and the "Default models" box connects to a purple "Distress Probability" box.
Figure 1
Simple Network Matrix example. This figure demonstrates a simple 3x3 network matrix. The entries of the matrix are x's subscripted with row then column numbers (e.g., x13). Every bank in the network has its own row and column; row sums show the total liabilities of the bank, while column sums show the total assets of the bank. The row sums and column sums are also shown in the figure as l's and a's subscripted with 1, 2, or 3.
Figure 2
Simple directed network example. Three large circles labeled 1, 2, and 3 represent the three banks in the network. Two arrows connect each pair of banks, pointing in opposite directions. For example, x13 points from bank 1 to bank 3, to demonstrate that bank 1 owes bank 3 money. The opposite arrow, x31, points from bank 3 to bank 1, to demonstrate that bank 3 owes bank 1 money.
Appendix A figure
This figure contains six images, each one showing the same network graph consisting of dots (nodes) connected by lines of connections. The differences in the distribution of node color across the images demonstrate how different network measures can capture different attributes of the network and draw attention to different regions in the images. Red is used to show high values of the measure, with a color scale moving down to dark blue for the lowest values.
The first column of three images shows degree centrality, closeness centrality, and betweenness centrality, respectively. The second column shows Eigenvector centrality, Katz centrality, and Alpha centrality, respectively.
In the degree centrality image (top left), most of the nodes are green, with a few distinct clusters of red nodes spread fairly evenly throughout the graph. There are almost no dark blue nodes.
In the closeness centrality image (top right), the colors radiate outwards. That is, the very center of the graph contains a circle of red, with concentric circles of yellow, green, and light blue moving outwards symmetrically. The corners of the graph are dark blue.
In the betweenness centrality image (middle left), there are almost no red nodes—just a few individual nodes colored red, which are not immediately noticeable. Most of the image is green, yellow, or orange, with a bit of dark blue at the edges. However, there do not seem to be any parts that stick out as a distinct color.
In the Eigenvector centrality image (middle right), there is a large cluster of red nodes at the top left of the graph. This is the largest red cluster in any of the six images. Otherwise, the graph is mostly green, with a bit of blue at the edges.
The Katz centrality image (bottom left) looks similar to the degree centrality graph, except the red and orange is a bit more diffused through the middle of the graph. There are no clusters that sharply stand out. The edges contain mostly green and light blue.
The alpha centrality graph (bottom right) has one very small cluster of red nodes in the top left; otherwise, the graph is all green, light blue, and dark blue. There are dense clusters of green nodes throughout, connected by blue nodes; this image contains the most dark blue nodes at the edges.