Table 1 Comparison of Ollivier-Ricci curvature (OR) with Forman-Ricci curvature (FR) or Augmented Forman-Ricci curvature (AFR) of edges in model and real networks.

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

Network

OR versus FR of edges

OR versus AFR of edges

Model networks

ER model with n = 1000, p = 0.003

0.89

0.90

ER model with n = 1000, p = 0.007

0.39

0.43

ER model with n = 1000, p = 0.01

−0.03

0.04

WS model with n = 1000, k = 2 and p = 0.5

0.92

0.92

WS model with n = 1000, k = 8 and p = 0.5

0.18

0.70

WS model with n = 1000, k = 10 and p = 0.5

0.10

0.69

BA model with n = 1000, m = 2

0.74

0.74

BA model with n = 1000, m = 4

0.33

0.36

BA model with n = 1000, m = 5

0.13

0.16

HGG model with n = 1000, k = 3, γ = 2, T = 0

0.78

0.66

HGG model with n = 1000, k = 5, γ = 2, T = 0

0.82

0.76

HGG model with n = 1000, k = 10, γ = 2, T = 0

0.85

0.87

Real networks

Autonomous systems

0.43

0.42

PGP

0.32

0.83

US Power Grid

0.60

0.76

Astrophysics co-authorship

0.25

0.70

Chicago Road

0.98

0.98

Yeast protein interactions

0.70

0.74

Euro Road

0.81

0.88

Human protein interactions

0.48

0.52

Hamsterster friendship

0.23

0.30

Email communication

0.19

0.53

PDZ domain interactions

0.72

0.71

Adjective-Noun adjacency

0.15

0.35

Dolphin

0.07

0.71

Contiguous US States

0.68

0.91

Zachary karate club

0.75

0.81

Jazz musicians

0.11

0.90

Zebra

−0.04

0.62

  1. In this table, we list the Spearman correlation between the edge curvatures. 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 S2 also contains results from additional analysis of model networks with an expanded set of chosen input parameters. Moreover, Supplementary Table S2 also lists the Pearson correlation between the edge curvatures in model and real networks.
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