Quantification of Spatial Parameters in 3D Cellular Constructs Using Graph Theory

Table 4

Quantitative metric statistics for different link thresholds for 3.0 × 10⁵ cells/mL collagen I hydrogel 24-hour timecourse.

	Time (hours)
	0	1	2	6	10	16	24
Average degree	1±0.21	0.9±0.19	1.05±0.18	1.54±0.31	1.85±0.35	2.6±0.46	4.15±0.67
Clustering coefficient	0.14±0.07	0.12±0.05	0.12±0.04	0.18±0.06	0.29±0.05	0.32±0.04	0.44±0.03
Average eccentricity	1.62±0.28	1.21±0.26	1.39±0.1	2.51±0.7	3.11±0.59	8.93±2.21	19.85±7.61
Maximum eccentricity (diameter)	7±0.64	5±0.05	5.33±0.64	7.78±1.69	10±1.26	15.44±2.36	29.58±7.93
Minimum eccentricity (radius)	0±0	0.33±0	0.33±0	0.11±0.19	1±0	1±0	4.25±2.47
Average eccentricity 90	1.57±0.29	1.17±0.25	1.37±0.12	2.39±0.59	2.87±0.48	7.57±1.8	16.64±6.55
Maximum eccentricity 90	6.78±0.67	4.78±0.63	5.22±0.5	7.55±1.32	9.11±0.96	14±2.06	27±7.12
Minimum eccentricity 90	0±0	0.33±0	0.33±0	0.11±0.19	1±0	1±0	3.5±1.89
Average path length (closeness)	1.07±0.17	0.85±0.15	0.97±0.09	1.56±0.34	1.82±0.29	4.35±0.84	10.22±3.81
Hop plot exponent	0.33±0.06	NAN±	0.36±0.03	0.49±0.08	0.52±0.09	0.7±0.08	1.15±0.11
Effective hop diameter	1.2E10	2.1E15	1.4E6±2E6	1.2E8±1E8	2E4±2.1E4	7E5±7.7E5	46.52±26.71
Giant connected ratio	0.15±0.03	0.11±0.02	0.11±0	0.11±0.03	0.12±0.02	0.35±0.06	0.68±0.29
Number of Connected Components	45.78±4.88	43.67±4.59	47.33±4.91	54.55±11.21	46.78±10.36	37.56±7.63	19.75±12.82
Percentage of isolated points	0.42±0.04	0.45±0.06	0.39±0.08	0.23±0.07	0.2±0.06	0.16±0.03	0.04±0.02
Percentage of end points	0.28±0.04	0.32±0.02	0.32±0.02	0.34±0.04	0.25±0.02	0.22±0.04	0.1±0.04
Number of central points	31.55±4.12	26.67±2.9	28.22±3.15	31.11±7.42	25±5.56	24.78±4.25	10.84±6.92
Percentage of central points	0.42±0.04	0.41±0.03	0.34±0.04	0.24±0.06	0.18±0.03	0.19±0.03	0.04±0.02
Number of nodes	83.33±28.87	74.33±30.01	85.33±13.43	140.67±42.19	144±42.51	174±99.8	307±57.03
Number of edges	48.75±10.22	40.25±8.66	47.84±7.61	121.75±22.6	146.92±26.65	297.34±49.57	659.33±106.32