(a) The quantities , , , and (normalized by their maximum values) as a function of the resolution parameter for a single time window beginning on 10 March 2005. The shaded gray area highlights the main plateau. The bottom curve gives the normalized variation of information between partitions at resolutions separated by . (b) The position of the main plateau at each time step, showing the main plateaus (i) containing and (ii) not containing .
(a) Observed fraction of time steps that the resolution lies in the main plateau. The vertical line indicates the value , which lies in the largest number of main plateaus and is the resolution at which we investigate the community dynamics. (b) (i) Normalized sampled distribution of the main plateau width and (ii) normalized sampled distribution of the -distance between the main plateau and . (c) (i) Distribution of normalized variation of information between the community configuration at and the configuration corresponding to the main plateau and (ii) distribution of normalized variation of information between consecutive time steps. The vertical lines give the mean when (left to right) 1, 2, 5, 10, and 20 nodes are randomly reassigned to different communities (averaged over 100 reassignments for each time step). (d) The fraction of time steps at which communities are observed. (e) The fraction of time steps at which a community of a given size is observed. (f) Comparison of the distribution of the scaled energy for (i) market data and (ii) 100 realizations of shuffled data.
(a) Mean community centrality vs the size of the community to which a node belongs. (b) Mean community alignment vs the betweenness centrality of nodes. (c) Mean community autocorrelation vs the projected community centrality. [All error bars indicate the standard error (Ref. 34).]
(a) Normalized distribution of link weights at each time step. (b) Scaled energy and standard deviation of the link weights. (c) Normalized variation of information between the community configurations at consecutive time steps. The horizontal lines show (from bottom to top) the mean of and 1, 2, 3, and 4 standard deviations above the mean. The vertical lines in (b) and (c) show the time steps when the following dates enter the rolling time window: 20 July 2007, 15 August 2007, and 16 December 2008 (two large reorganizations at consecutive time steps are marked by circles following this date). (d) Carry trade index . The vertical line shows 15 August 2007 and the shaded blocks (from left to right) indicate Q3 2007, Q4 2007, Q1 2008, and Q4 2008.
Schematic representation of the change in the community configuration in one half of the FX market network following: (a) 15 August 2007, when there was significant unwinding of the carry trade and (b) 16 December 2008, when the U.S. Federal Reserve cut the funding interest rate from 1% to 0%–0.25%. The node colors after the community reorganization correspond to the community assignments before the change. If the parent community of a post-reorganization community is obvious, it is drawn in the same color as its parent. The nodes represented as triangles resided in the opposite half of the network before the community reorganization.
Quarterly node role evolutions in the plane.
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