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

EPJ Data Science

Table 3 Summary of average statistics for the empirical and optimal simulated networks

	\(\boldsymbol{\left \langle k \right \rangle ^{\mathrm{OBS}}}\)	\(\boldsymbol{\left \langle l \right \rangle ^{\mathrm{OBS}}}\)	\(\boldsymbol{C^{\mathrm{OBS}}}\)	\(\boldsymbol{\varepsilon ^{0}}\)	\(\boldsymbol {\left \langle k \right \rangle ^{*}}\)	\(\boldsymbol{\left \langle l \right \rangle ^{*}}\)	\(\boldsymbol{C^{*}}\)
Aggregated R&D network	2.74	5.41	0.101	2%	2.76	5.33	0.098
Sectoral R&D networks
Pharmaceuticals (SIC 283)	3.14	4.94	0.097	2%	3.13	4.95	0.097
Computer hardware (SIC 357)	5.12	3.70	0.161	6%	5.37	3.59	0.175
Communications equipment (SIC 366)	4.81	3.75	0.203	2%	4.83	3.76	0.210
Electronic components (SIC 367)	4.65	3.80	0.168	2%	4.76	3.83	0.174
Computer software (SIC 737)	3.47	4.33	0.138	3%	3.56	4.27	0.141
R&D, laboratory and testing (SIC 873)	3.37	5.15	0.205	3%	3.30	5.22	0.200
Co-authorship networks
Quant. mech., field theor., spec. relativity (PACS 03)	5.22	6.43	0.379	12%	5.83	5.58	0.392
General relativity and gravitation (PACS 04)	7.84	6.27	0.666	>30%	16.64	4.39	0.535
Optics (PACS 42)	6.92	6.40	0.425	10%	7.60	5.79	0.451
Electronic transport in condensed matter (PACS 72)	5.73	7.06	0.448	8%	6.15	6.58	0.471
Superconductivity (PACS 74)	7.05	5.87	0.443	7%	7.51	5.51	0.465
Other areas of applied and interdisciplin. physics (PACS 89)	3.60	8.28	0.462	8%	3.82	7.82	0.501

For the empirical collaboration networks, we report the average degree, \(\left \langle k \right \rangle ^{\mathrm{OBS}}\), average path length, \(\left \langle l \right \rangle ^{\mathrm{OBS}}\), and global clustering coefficient, \(C^{\mathrm{OBS}}\). For optimal simulated network, we report the mean values over the 25 network realizations of average degree, \(\left \langle k \right \rangle ^{*}\), average path length, \(\left \langle l \right \rangle ^{*}\) and global clustering coefficient, \(C^{*}\). We also report the error threshold or accuracy \(\varepsilon ^{0}\).