Table 3 Comparison of Ollivier-Ricci curvature (OR), Forman-Ricci curvature (FR) and Augmented Forman-Ricci curvature (AFR) of edges with other edge-based measures, edge betweenness centrality (EBC), embeddedness (EMB) and dispersion (DIS), in model and real networks. In this table, we list the Spearman correlation between the edge-based measures.

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

Network	OR versus			FR versus			AFR versus
Network	EBC	EMB	DIS	EBC	EMB	DIS	EBC	EMB	DIS
Model networks
ER model with n = 1000, p = 0.003	−0.86	0.08	0.00	−0.81	−0.07	0.00	−0.82	0.04	0.00
ER model with n = 1000, p = 0.007	−0.53	0.25	0.05	−0.80	−0.11	−0.03	−0.82	0.06	0.02
ER model with n = 1000, p = 0.01	−0.34	0.32	0.10	−0.76	−0.13	−0.05	−0.79	0.07	0.03
WS model with n = 1000, k = 2 and p = 0.5	−0.75	0.00	0.00	−0.57	0.00	0.00	−0.57	0.00	0.00
WS model with n = 1000, k = 8 and p = 0.5	−0.85	0.79	0.44	−0.52	−0.05	−0.08	−0.89	0.68	0.42
WS model with n = 1000, k = 10 and p = 0.5	−0.87	0.82	0.49	−0.45	−0.05	−0.07	−0.89	0.73	0.47
BA model with n = 1000, m = 2	−0.73	−0.09	−0.11	−0.76	−0.30	−0.16	−0.77	−0.26	−0.15
BA model with n = 1000, m = 4	−0.45	0.18	0.14	−0.83	−0.48	−0.35	−0.84	−0.43	−0.33
BA model with n = 1000, m = 5	−0.30	0.30	0.25	−0.85	−0.54	−0.41	−0.86	−0.48	−0.39
HGG model with n = 1000, k = 3, γ = 2, T = 0	−0.47	−0.30	−0.15	−0.67	−0.04	−0.18	−0.76	0.27	−0.07
HGG model with n = 1000, k = 5, γ = 2, T = 0	−0.62	−0.20	−0.13	−0.73	−0.08	−0.17	−0.81	0.20	−0.10
HGG model with n = 1000, k = 10, γ = 2, T = 0	−0.78	−0.03	−0.06	−0.79	−0.15	−0.12	−0.87	0.14	−0.08
Real networks
Autonomous systems	−0.17	−0.37	−0.25	−0.26	−0.44	−0.18	−0.27	−0.41	−0.16
PGP	−0.64	0.20	−0.13	0.11	−0.69	−0.17	−0.56	0.21	−0.15
US Power Grid	−0.61	0.16	0.06	−0.26	−0.41	−0.19	−0.45	0.09	0.04
Astrophysics co-authorship	−0.78	0.47	−0.16	−0.23	−0.58	−0.23	−0.63	0.07	−0.27
Chicago Road	−0.65	0.00	0.00	−0.65	0.00	0.00	−0.65	0.00	0.00
Yeast protein interactions	−0.83	0.06	−0.01	−0.52	−0.15	−0.13	−0.59	0.14	0.00
Euro Road	−0.54	0.05	0.02	−0.40	−0.31	−0.07	−0.43	0.00	0.03
Human protein interactions	−0.46	0.07	0.01	−0.38	−0.22	−0.19	−0.43	−0.07	−0.10
Hamsterster friendship	−0.53	0.12	0.00	−0.35	−0.61	−0.40	−0.42	−0.47	−0.32
Email communication	−0.61	0.55	0.24	−0.32	−0.45	−0.41	−0.57	0.01	−0.16
PDZ domain interactions	−0.79	−0.04	0.00	−0.55	−0.02	0.00	−0.55	0.06	0.00
Adjective−Noun adjacency	−0.51	0.22	0.09	−0.42	−0.72	−0.55	−0.57	−0.42	−0.37
Dolphin	−0.66	0.51	0.28	0.11	−0.58	−0.21	−0.61	0.59	0.31
Contiguous US States	−0.68	−0.10	−0.15	−0.49	−0.72	−0.71	−0.64	−0.03	−0.08
Zachary karate club	−0.79	0.10	−0.06	−0.64	−0.29	−0.37	−0.80	0.43	0.14
Jazz musicians	−0.84	0.57	−0.03	−0.22	−0.66	−0.18	−0.76	0.47	−0.05
Zebra	−0.94	0.52	0.13	0.04	−0.71	−0.15	−0.65	0.97	0.09

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 S4 also contains results from additional analysis of model networks with an expanded set of chosen input parameters. Moreover, Supplementary Table S4 also lists the Pearson correlation between the edge-based measures in model and real networks.

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