Data-driven modeling of collaboration networks: a cross-domain analysis

EPJ Data Science

Table 2 Optimal sets of probabilities to simulated the collaboration networks

	\(\boldsymbol{p^{*L}_{s}}\)	\(\boldsymbol{p^{*L}_{d}}\)	\(\boldsymbol {p^{*L}_{n}}\)	\(\boldsymbol{p^{*N L}_{l}}\)	\(\boldsymbol{p^{*N L}_{nl}}\)
Aggregated R&D network	0.30	0.30	0.40	0.75	0.25
Sectoral R&D networks
Pharmaceuticals (SIC 283)	0.35	0.35	0.30	0.80	0.20
Computer hardware (SIC 357)	0.55	0.30	0.15	0.90	0.10
Communications equipment (SIC 366)	0.75	0.15	0.10	0.80	0.20
Electronic components (SIC 367)	0.65	0.20	0.15	0.90	0.10
Computer software (SIC 737)	0.55	0.20	0.25	0.95	0.05
R&D, laboratory and testing (SIC 873)	0.40	0.40	0.20	0.20	0.80
Co-authorship networks
Quant. mech., field theor., spec. relativity (PACS 03)	0.85	0.05	0.10	0.45	0.55
General relativity and gravitation (PACS 04)^†	0.50	0.05	0.45	0.05	0.95
Optics (PACS 42)	0.60	0.05	0.35	0.35	0.65
Electronic transport in condensed matter (PACS 72)	0.50	0.05	0.45	0.30	0.70
Superconductivity (PACS 74)	0.55	0.05	0.40	0.35	0.65
Other applied and interdisciplinary physics (PACS 89)	0.65	0.05	0.30	0.25	0.75

The optimal probabilities are indicated using ^∗. Recall that the probability of a labeled agent to select an agent with the same label is \(p^{L}_{s}\), to select an agent with a different label is \(p^{L}_{d}\) and to select a non-labeled agent is \(p^{L}_{n}\). While, the probability of a non-labeled agent to select a labeled agent is \(p^{N L}_{l}\) and to select a non-labeled agent is \(p^{N L}_{nl}\). The probabilities \(p^{L}_{s}\), \(p^{L}_{d}\) and \(p^{L}_{n}\) sum up to 1; likewise, \(p^{N L}_{l}\) and \(p^{N L}_{nl}\) sum up to 1. ^†Only for the co-authorship network in general relativity and gravitation (PACS 04) the model is unable to generate a network matching all the three measures \(\left \langle k \right \rangle \), \(\left \langle l \right \rangle \) and C at the same time. Only \(\left \langle l \right \rangle \) and C can be retrieved with an accuracy of 30%, while the generated \(\left \langle k \right \rangle \) is not compatible with the empirical measure. Even though we report these values for completeness, they cannot be considered representative of the real network.