Table 4 Comparison of Ollivier-Ricci curvature (OR), Forman-Ricci curvature (FR) and Augmented Forman-Ricci curvature (AFR) of vertices with other vertex-based measures, degree, betweenness centrality (BC) and clustering coefficient (CC), in model and real networks.

From: Comparative analysis of two discretizations of Ricci curvature for complex networks

Network	OR versus			FR versus			AFR versus
Network	Degree	BC	CC	Degree	BC	CC	Degree	BC	CC
Model networks
ER model with n = 1000, p = 0.003	−0.94	−0.94	−0.07	−0.94	−0.94	−0.13	−0.94	−0.94	−0.08
ER model with n = 1000, p = 0.007	−0.98	−0.98	−0.18	−0.99	−0.98	−0.26	−0.99	−0.98	−0.21
ER model with n = 1000, p = 0.01	−0.98	−0.98	−0.16	−0.99	−0.98	−0.25	−0.99	−0.98	−0.21
WS model with n = 1000, k = 2 and p = 0.5	−0.71	−0.82	0.00	−0.75	−0.73	0.00	−0.75	−0.73	0.00
WS model with n = 1000, k = 8 and p = 0.5	−0.81	−0.96	0.51	−0.98	−0.91	0.05	−0.91	−0.98	0.38
WS model with n = 1000, k = 10 and p = 0.5	−0.79	−0.95	0.57	−0.99	−0.91	0.09	−0.92	−0.98	0.41
BA model with n = 1000, m = 2	−0.90	−0.90	−0.18	−0.59	−0.77	−0.39	−0.59	−0.78	−0.37
BA model with n = 1000, m = 4	−0.94	−0.88	−0.08	−0.73	−0.84	−0.49	−0.73	−0.85	−0.45
BA model with n = 1000, m = 5	−0.94	−0.90	−0.05	−0.78	−0.85	−0.40	−0.79	−0.86	−0.37
HGG model with n = 1000, k = 3, γ = 2, T = 0	−0.28	−0.30	−0.14	−0.86	−0.60	−0.45	−0.79	−0.58	−0.37
HGG model with n = 1000, k = 5, γ = 2, T = 0	−0.15	−0.17	−0.03	−0.89	−0.61	−0.21	−0.85	−0.60	−0.18
HGG model with n = 1000, k = 10, γ = 2, T = 0	0.06	−0.06	0.01	−0.93	−0.68	0.31	−0.91	−0.66	0.30
Real networks
Autonomous systems	−0.85	−0.70	−0.39	−0.51	−0.38	−0.55	−0.50	−0.38	−0.55
PGP	−0.12	−0.49	0.29	−0.73	−0.51	−0.51	−0.35	−0.46	−0.05
US Power Grid	−0.68	−0.80	0.03	−0.79	−0.62	−0.49	−0.69	−0.68	−0.13
Astrophysics co-authorship	−0.39	−0.72	0.62	−0.95	−0.64	0.25	−0.64	−0.66	0.41
Chicago Road	−0.33	−0.34	0.00	−0.42	−0.42	0.00	−0.42	−0.42	0.00
Yeast protein interactions	−0.54	−0.67	−0.05	−0.57	−0.56	−0.33	−0.45	−0.54	−0.07
Euro Road	−0.82	−0.75	−0.22	−0.82	−0.64	−0.38	−0.80	−0.65	−0.24
Human protein interactions	−0.77	−0.78	−0.23	−0.71	−0.65	−0.43	−0.67	−0.64	−0.34
Hamsterster friendship	−0.87	−0.87	−0.30	−0.92	−0.76	−0.45	−0.91	−0.76	−0.42
Email communication	−0.80	−0.88	0.06	−0.97	−0.87	−0.31	−0.93	−0.88	−0.19
PDZ domain interactions	−0.50	−0.58	−0.12	−0.62	−0.64	−0.14	−0.61	−0.64	−0.09
Adjective-Noun adjacency	−0.57	−0.76	0.07	−0.96	−0.84	−0.50	−0.95	−0.84	−0.45
Dolphin	−0.04	−0.39	0.44	−0.98	−0.77	−0.45	−0.73	−0.72	−0.04
Contiguous US States	−0.59	−0.74	0.71	−0.98	−0.82	0.55	−0.78	−0.79	0.70
Zachary karate club	0.10	−0.09	0.35	−0.84	−0.76	0.40	−0.47	−0.60	0.52
Jazz musicians	0.78	0.34	0.08	−0.99	−0.72	0.33	−0.49	−0.56	0.56
Zebra	0.78	0.35	−0.33	−0.94	−0.73	0.70	0.76	0.33	−0.31

In this table, we list the Spearman correlation between the vertex-based measures. In case of model networks, the reported correlation is mean (rounded off to two decimal places) over a sample of 100 networks generated with specific input parameters. Supplementary Table S5 also contains results from additional analysis of model networks with an expanded set of chosen input parameters. Moreover, Supplementary Table S5 also lists the Pearson correlation between the vertex-based measures in model and real networks.

Back to article page

Table 4 Comparison of Ollivier-Ricci curvature (OR), Forman-Ricci curvature (FR) and Augmented Forman-Ricci curvature (AFR) of vertices with other vertex-based measures, degree, betweenness centrality (BC) and clustering coefficient (CC), in model and real networks.

Search

Quick links