Table 1. Comparison of network robustness measures.
We provide the average Ricci curvature, average global network entropy, average shortest path, and average graph diameter computed over a period of 1 year beginning with 1 January of each year with a window T = 22 days and a threshold of ξ = 0.85. As seen in the graph, a correlation between curvature and well-known measures of fragility.
| Measure |
Jan 1998 |
Jan 1999 |
Jan 2000 |
Jan 2001 |
Jan 2002 |
Jan 2003 |
Jan 2004 |
Jan 2005 |
Jan 2006 |
Jan 2007 |
Jan 2008 |
Jan 2009 |
Jan 2010 |
Jan 2011 |
Jan 2012 |
| Curvature | −0.297 | −0.304 | −0.285 | −0.218 | −0.0166 | −0.256 | −0.253 | −0.214 | −0.245 | −0.218 | −0.068 | −0.141 | −0.101 | 0.023 | −0.0255 |
| Entropy | 0.941 | 0.862 | 0.909 | 1.123 | 1.505 | 1.193 | 1.022 | 1.128 | 1.066 | 1.316 | 2.159 | 1.745 | 2.105 | 2.688 | 1.282 |
| Shortest path | 12.412 | 13.811 | 14.910 | 12.951 | 9.362 | 10.199 | 12.291 | 11.845 | 12.413 | 9.636 | 7.186 | 8.060 | 7.469 | 6.208 | 9.545 |
| Diameter | 31.361 | 34.726 | 38.210 | 33.186 | 25.500 | 27.397 | 31.250 | 29.929 | 31.494 | 25.064 | 21.044 | 22.480 | 20.964 | 17.770 | 25.144 |