Temporal network analysis

This page follows analyses and recreates some plots from Schulz J et al. (2017) PLOS ONE 12(6): e0179915.

Basic network summary

Network size

Overall network size: 170 holdings active over the observed time period

month	holdings active (n)	holdings active (prop.)
Jan 2019	29	0.171
Feb 2019	10	0.059
Mar 2019	8	0.047
Apr 2019	15	0.088
May 2019	6	0.035
Jun 2019	16	0.094
Jul 2019	22	0.129
Aug 2019	20	0.118
Sep 2019	18	0.106
Oct 2019	22	0.129
Nov 2019	14	0.082
Dec 2019	18	0.106

Holdings active (n)

Holdings active (prop)

Movements and edges

Overall number of movements: 100 movements over the observed time period
Overall number of edges: 100 different links between holdings over the observed time period
Overall edge density: 0.003 of all possible links between holdings are observed over the observed time period

month	movements (n)	movements (prop.)	edges (n)	edges (prop.)	edge density (prop.)
Jan 2019	15	0.150	15	0.150	0.001
Feb 2019	5	0.050	5	0.050	0.000
Mar 2019	4	0.040	4	0.040	0.000
Apr 2019	8	0.080	8	0.080	0.000
May 2019	3	0.030	3	0.030	0.000
Jun 2019	8	0.080	8	0.080	0.000
Jul 2019	11	0.110	11	0.110	0.000
Aug 2019	10	0.100	10	0.100	0.000
Sep 2019	9	0.090	9	0.090	0.000
Oct 2019	11	0.110	11	0.110	0.000
Nov 2019	7	0.070	7	0.070	0.000
Dec 2019	9	0.090	9	0.090	0.000

Movements

Movements (prop.)

Edges

Edges (prop.)

Density

Movement weights (batch sizes)

month	min	Q1	median	mean	Q3	max
Jan 2019	42	54.50	74.0	91.800	115.50	185
Feb 2019	46	73.00	97.0	96.800	108.00	160
Mar 2019	30	39.75	50.5	64.250	75.00	126
Apr 2019	33	39.75	53.5	75.500	98.50	157
May 2019	89	101.00	113.0	128.333	148.00	183
Jun 2019	59	120.75	140.0	132.000	162.00	178
Jul 2019	39	71.50	90.0	99.182	123.50	181
Aug 2019	31	51.50	104.5	98.800	128.25	177
Sep 2019	41	108.00	122.0	124.778	147.00	183
Oct 2019	47	90.50	125.0	124.455	166.00	187
Nov 2019	76	116.50	134.0	135.143	159.00	185
Dec 2019	42	65.00	151.0	123.556	159.00	172

Static network analysis (monthly snapshots)

Component analysis

The largest giant strongly connected component (GSCC) is the largest number of nodes (holdings) that can all reach each other by some directed path of movements. This means that any node in that set could indirectly infect any other, or that a single source outbreak within the component could theoretically infect anything else within that component.

The giant in-component (GIC) consists of all nodes (holdings) that can reach the GSCC, but are not part of it, because there is no directed path from the GSCC to these nodes. This means that any holding in this set could infect holdings in the GSCC, but not be infected by them.

Conversely, the giant out-component (GOC) consists of all nodes (holdings) that can be reached from the GSCC, but are not part of it, because there is no directed path from these nodes to the GSCC. This means that any holding in this set could be infected by holdings in the GSCC, but not infect them.

Loyalty

This is a measure of consistency in the network between different points in time. Darker colours indicate a larger proportion of trades that are in common between two months. The black diagonal indicates that each month’s movements are identical to themselves.